How to calculate the spectral response of a spectrograph


The spectral response to the incident optical flux is a function that expresses the way in which the instrumental ensemble (telescope + spectrograph) reacts to the optical flux in question. The result depends on the wavelength. The knowledge of the instrumental response allows, from the signal recorded by the detector, to find the true signal of the star observed by correcting the radiometric biases induced by the equipment. Calculating the instrument response is therefore an important step in the spectrum calibration procedure.

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This article describes several practical methods to arrive at the value of the instrument response. I support the demonstration on data acquired with a spectrograph UVEX (300 lines / mm, 25 micron clear slit, camera ASI183MM) mounted on a telescope Ritchey-Chrétien (RC) of 25.4 cm f/8. However, the algorithms presented are of a general nature and apply to the processing of data acquired by any other spectrograph (LISA, Alpy, etc.). I use ISIS 5.9.6 (b) and upper to perform spectra reduction.

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Very often the discussions around how to calculate the instrumental response are sources of confusion, mainly because the terms of the problem are badly posed. Let’s try to put things in order.

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The apparent signal measured by the detector from a star at a given wavelength is the result of the product of several terms:

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             “Apparent Signal” = “Real Signal” x “Atmospheric Transmission” x “Instrument Response” x “Calibration Coefficient”

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with:

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  • • “Apparent signal”, the measured signal, usually expressed in digital numbers (or ADU, or Analog Digital Unit).
  • • “Real signal”, the absolute spectral flux of the star (expressed in physical unit, for example in erg / cm2 / s / A).
  • • “Atmospheric transmission », the spectral coefficient of optical transmission of the atmosphere in the intended direction of the sky and for the time of observation.
  • • “Instrument response », the instrument response itself.
  • • “Calibration Coefficient”, the absolute calibration coefficient of the instrument that allows digital values to be attached to physical flow units.

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Here we will ignore the absolute calibration coefficient, the evaluation of which is a subject in its own right. We will therefore work on relative intensity data.

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Note: we could add another term concerning atmospheric spectral dispersion — see for example the discussion here — whose consequences can be dramatic with a slit spectrograph under some circumstances (for a high parallactic angle, for low spectral resolution spectroscopy). It is assumed here that one observes near the local meridian or near the zenith, or that one adopts an instrumental configuration which eliminates the effect of the wavelength differential atmospheric refraction, which will be the object of a future article.

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It is quite common for the instrument response to be equated with the result of the product “Atmospheric Transmission” x “Instrument Response”. It is here that problems arise because this is cause of misunderstanding in many cases. It is indeed necessary to distinguish what is variable from one observation to another, in this case the atmosphere, of what is constant, in this case the instrument. There is indeed no reason (except false manipulation) that the characteristics of the instrument change according to the pointed target. This is a crucial point: the true response is a fixed and specific characteristic of the instrument used. If you evaluate it in a specific observation (a instrumental calibration session), this result will be valid for « all » other science observations, including those made several days or months after this calibration, and also whatever the place of the sky pointed. The condition is of course that the instrument is not deeply modified in this period of time. It is this initial calibration procedure that I discuss here, but also its application on examples.

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I propose you two techniques to arrive at a good result. The first, so-called “short” is to use an economical artificial light source to find the instrument response. She is expeditious. The second is longer to apply because it uses a natural source, the light of the stars. We suspect it, I call it “long” method. It is more rigorous and also essential for calibrating the spectra in the far blue or ultraviolet (UV), which will be of interest to users of spectrographs such as UVEX.

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1. Short method

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The short  method is entirely based on the realization of a “spectral flat-field”. It consists in taking the spectrum of a source emitting a continuous spectrum (without lines, uniform along wavelength) under the “normal” conditions of observation. The ideal is to use a halogen-type tungsten filament lamp. The spectral distribution of the emitted light then closely follows that of a black body whose temperature is close to 2700-2900K depending on the chosen lamp model.

In order to have the choice of lamp type, my method is to manually shake during the exposure time a halogen lamp in front of the telescope entrance aperture. This agitation is important because then the light arrives from all parts of the telescope pupil in the integrated spectral image. It may find that the detector saturates at the end of the exposure time, which is typically a few seconds. With a CMOS camera, such as the ASI183MM used here, it is possible to adjust the gain to the minimum to increase the dynamics range and reduce the risk of saturation, which is not possible to make a CCD camera. We can also consider having a white screen or a diffuser in front of the telescope that is illuminated with the lamp (be careful, tracing paper tends to eliminate blue photons, and more, UV).

But why not use the “white” lamp of many spectrographs in their integrated calibration system? As I said above, to have the choice of the light source, which is essential to the method. It is important to have a good idea of the spectral distribution of this calibration means. This is not usually the case with the calibration system supplied by the manufacturers. And even though this distribution is known, it is unfortunately often so heckled, as in the case of the spectrograph Alpy600, which is not easy to exploit. I also add that having the source at the entrance of the telescope (after shaking) makes it possible to work at the same F/D ratio as during the observation of the stars, which eliminates some calibration bias (think you can also use a diffusing screen if the observation in the far blue is not your first concern). To those who find that “agitate” a lamp in front of a telescope is not very serious, that it is “rustic” and binding, I answer that the operation is to be done only once during the ” life “of the instrument (to make it simple), and that therefore, it does not require a big effort considering the gain that represents then. And as long as it works … It is even possible to achieve this “flat-field” acquisition  while the optical tube is placed on a table if it is removable (so a “lab” measure , on which one can spend time).

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Here is the typical spectral image acquired under these conditions (the image named « tung_2D », for example):

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The result is really characteristic of the observation of a domestic tungsten lamp: a very strong variation of the signal measured between the blue part of the spectrum (on the left) and the red part (on the right). Because of its color temperature, this type of lamp generates indeed more red photons than blue photons. The oscillations observed in the red are related to a rather rapid variation in the quantum efficiency of the Sony IMX183 detector that equips the camera, a characteristic that must be carefully considered when calculating the instrument response.

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I recommend acquiring 10 to 20 flat-field images of this type. Under ISIS, process this spectrum sequence in the usual way as if it were to observe an object having an extended surface, a nebula for example. It is necessary to have beforehand establish the spectral calibration law ( pixel -> wavelength relation) and to synthesize the offset and dark master images. The binning zone should be wide to maximize the signal-to-noise ratio (SNR) in the calculated spectral profile (see image above). The “General” tab of ISIS should be filled in the following manner, which is typical for extracting spectrum from a wide angular source, which occupies the full height of the slot:

The spectral profile extracted is found at opposite. The signal is indeed weak in blue, maximum in the orange part, and we find our famous quantum efficiency oscillations (all the photonic sensors generate this kind of things, but in varying degrees).

At least for the visible wavelength,  the spectral distribution of the radiation produced by a simple tungsten filament lamp, costing a few euros only, reveals extremely close to a black body radiation  (a thermal emission). We will exploit this property.

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ISIS offers a large number of tools that can be used from the command line (“Tools” tab, then “Commands”), the reason being not to overload the graphical interface. One of these commands is used to calculate the Planck profile of a black body from a temperature in Kelvin that is provided in parameters. This is the L_PLANCK command, so here is the syntax:

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l_planck [file] [temperature] [lambda1] [Lambda2] [step]

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with [file], the name of the Planck profile that the function will produce in the working directory in FITS format, [temperature], the black body temperature in Kelvin, [lambda1] and [lambda2], the wavelength limits from the product profile and [step], the wavelength step in the file.

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Here I use a halogen lamp whose color temperature is given 2900 K by the manufacturer (in your purchases, look for a lamp with the highest color temperature possible for maximum signal in the blue). In my example, the parameters are:

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After <return> the file “planck.fits” is produced with a step of 0.5 angstrom. Here is the spectral profile in question:

At this stage we have available on one side the measured spectrum of the lamp, which I call “lamp signal”, on the other side the spectral distribution in the light emitted by the lamp, the “black body profile”. The calculation of the instrument response is therefore trivial. It consists of dividing the first profile by the second:

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“Instrument response” = “lamp signal” / “black body profile”

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Note: this operation on two spectra can be done in ISIS several ways. For example, load the measured intensity profile of the lamp from the “Profile” tab and from the “Arithmetic” tool, fill in the “Divide by profile” field with the name “planck” and then “Apply”.

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Here is the instrument response thus calculated:

The way to get this calibration file, which I will later call « direct_response” is very simple. I will show later, at the moment of exploiting it, that this result is quite honest.

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It should be noted that this curve is the result of the product of optical transmission of the telescope, transmission of the spectrograph, the efficiency of the diffraction grating, the quantum efficiency of the detector (but not the atmosphere). It can be seen that the overall relative efficiency of the instrument is maximum around 5000 A, but remains high in the blue, which is a characteristic of the UVEX spectrograph (the decrease in UV is partly related to the RC mirror coatings). We also note the oscillations of the detector quantum efficiency, well present and therefore taken into account to correct the spectral data to be processed.

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This “short” method is based entirely on the trust we know in the spectral distribution of the lamp But a halogen lamp of 2800K or 2900K produces a very insufficient number of photons to calibrate the UV part of the spectrum, which is a necessity with the UVEX spectrograph if we wish to exploit it in this part of the spectrum (it is not an obligation of course!). The « long » method will correct these difficulties.

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But before addressing this second part, a note about accuracy of « response direct » evaluation…

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Very often, the stray light produced by the optics of the spectrograph (scattering phenomenon on the components) produces a luminous background which potentially biases our result. The proof, in the parts of the image situated outside the zone illuminated by the slit, the signal is not strictly null. A bias (false zero) therefore potentially affects the calculated response profile. It can be corrected at least in part by considering “out of slit » areas with sky background areas. With this information, under ISIS, uncheck the box “Background sky not removed” in the “General” tab, then adjust the calculation areas of the sky background (“Calibration” tab) as shown in the screenshot below:

Then process the spectrum as before.

2. Long method

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We will now use a light source which is a priori more reliable and produces a much whiter light than a tungsten lamp, or even a rather blue light. It will be the light coming from the stars themselves, and more particularly from the hot stars of A or B spectral type.

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During an intermediate stage of the treatment we will also need the instrument response  calculated during “short” method, the profile “direct_response”, and that does not pose very particular difficulties. So, the “long” method is actually a mixed method.

We use here the star Vega as a source of natural light, an A0V type object, whose spectral profile is well known (up to the UV, which is important when working with UVEX). Attention, it is necessary to observe with the minimal gain of a CMOS camera to put a long exposure regarding the atmospheric agitation, and also to average a large number of individual acquisitions. With a fixed gain CCD camera, an equivalent spectral type source (A or B) of lower brightness must be found in the MILES database for example. On the left, the apparent spectrum, without having applied instrument response correction, since considered unknown at this stage. This profile is called “vega_raw » (for example).

The next step is to temporarily divide the Vega star raw spectrum by the “direct_response” file. The latter is assimilated here to the pre-response of the instrument. The result is on the right, and it’s called “vega1” (this is an example). The performed operation is thus: “vega1” = “vega_raw » / “direct_response”. This work makes it possible to remove the « medium-frequency” variations from the apparent spectrum of the star, in particular here the oscillations of the quantum efficiency of the detector. This will make it possible to find the final instrument response more simply (note that the continuum is much smoother, except of course presence of Balmer lines).

The theoretical (or expected) spectrum of Vega is then recovered from the ISIS spectral database. I recommend the profile from the CALSPEC spectrophotometric base because it covers the ultraviolet, which is ideal for UVEX. This spectrum is called (see right) “vega_theoretical”. This is the true profile of the star outside the atmosphere, as we would like our instrument to restore it after data reduction in the ideal.

The next step is to divide the “vega1” spectrum by the “vega_theoretical” spectrum. The result is the spectrum that is called here “vega2”. The Balmer spectral lines theoretically must disappear. In this case, our spectrum UVEX is slightly more resolve than the CALSPEC database, also before the division, the UVEX spectrum is slightly degraded by filtering it with the tool “Filter” of “Profile” tab (convolution by a Gaussian function). The filtering parameter is found by successive tests so that in the “vega2” spectrum the residue of the Balmer lines is the least visible possible. The result is never perfect (the spectral line function of the instrument always produces distortions in the profile of the lines), but to do the best. It is also the moment to verify that the wavelength spectral calibration is correct (absence of marked local gradient effect, it is a severe test!).

The artifacts residual  of the “vega2” profile are then erased by interactive smoothing with the help of the “Continuum” tool. Here again we need fingering for this operation, difficult to achieve otherwise than the hand. The goal is to eliminate the asperities that are obviously foreign to the instrumental response (asperities at the level of Balmer lines,  telluric lines), while maintaining the low-frequency variations specific to the effective response. The result, named “vega3”, is shown at right.

The intermediate spectrum “vega3” is now multiplied by the file “direct_response” to take into account the « medium-frequency” characteristics of the instrument response (remember, in a previous step we divided by the file “direct_response” and here we do the opposite operation to return to the original situation somehow). The result spectrum is very close to the desired response (see right). It is called for the moment “vega4” and therefore, “vega4” = “vega3” x “direct_response”.

Take care, the “vega4” file is not yet the desired instrument response because some light energy of the star is lost through the atmosphere, and we have not considered until then. This prevents us from getting the pure instrument response at this stage (see the fundamental equation at the beginning of this article). To achieve this, we must compensate the effect of the atmosphere by calculating the spectral transmission in the direction of Vega star at the time of observation.

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As is often the case in ISIS, there are several ways to perform this type of calculation. The “official” version first consists in finding the Vega star elevation above the horizon at the observation time from the “Heliocentric velocity » tab of the “Miscellaneous” tab. Here be careful to fill the fields “Longitude” and “Latitude” of the place of observation in the tab “Configuration”. Also use Universal Time to date your observations. The actual atmospheric transmission is then calculated from the “Miscellaneous” -> “Atmosphere” tab. The previously calculated angular elevation and an idea of AOD (horizontal transparency) must be provided. We are on May 13, 2019 during this observation, with a fairly clear night in a semi-urban, I adopted the value typical value for this period and situation, AOD = 0.1.

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There is a trick to get faster to the atmospheric transmission using the processing of Vega spectrum:

From the “General” tab, tell ISIS to calculate the atmospheric transmission and apply it when processing the spectra. ISIS then searches for you the coordinates of the star in SIMBAD from the name you give in the “Object” field, then calculates the elevation and finally the transmission. Run the processing…

In the course of the operations, you notice that ISIS calculates the atmosphere transmission (at the time of the observation Vega was almost at the zenith — see angular elevation : 84,8 deg.).

The software produces in the working directory the file “atmo_Vega”: it is the atmospheric transmission. Everything is done automatically.

The atmospheric transmission calculated for an ADO of 0.1 (“atmo_Vega” file).

And here’s the finishing touch: dividing the “vega4” profile by the atmospheric transmission, we get the instrument response, as if it were operated outside the atmosphere, as if it were embedded on an artificial satellite. This is the real instrument response – see the curve at right It is called “inst_response”. So we made “reponse_inst” = “vega4” / “atmo_Vega”.

It is very instructive to compare the response found by the “short” method, by exploiting the single tungsten lamp, and the response found by the “long” method by exploiting the light of a star – see opposite. The difference is relatively small, which validates both methods. It is impressive to see the effectiveness of the “short” method in view of the simplicity of the means employed.

But for an accurate diagnosis of the quality of the one and other instrument response found, it is necessary to reduce the spectrum of our Vega star with the respective response curves. To do this, simply fill in the “Instrument response” field of the “General” tab with the name of the file of your choice (either “direct_response” or “inst_response”, see the example opposite). Of course, one must think of correcting the spectra of atmospheric transmission so that the calculated profile corresponds to an observation from space.

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Tip: if you do not have an Internet connection or if the object is not found on SIMBAD, you can always calculate the atmospheric transmission by hand and give the result name in the field « Atmo. transmission »:

Be careful, you should NOT select “Automatic air mass” option. If you select this option, the atmospheric transmission to be supplied is that corresponding to a zenital transmission (“atmo_Vega_z0” for example).

The graphs below make it possible to compare the calculated Vega profile of the Vega in the two situations with the expected theoretical spectrum (MILES spectrum):

By processing with the response found via the “short method”, so without reference to any natural source, a discrepancy appears between the observed spectrum and the expected spectrum. This discrepancy is detrimental when performing precision spectrophotometric work, but the technical approach appears as a reasonable troubleshooting solution. Especially for users of UVEX, the analysis has been pushed up to 3250 A. In the UV, the situation is much more problematic. The fact that the tungsten lamp used produces almost no photon is paid down 3600 A.

Spectrum calculated using the “long method” response. This one sticks is very nearly similar to the theoretical spectrum. This is not surprising since we observe here the star that served as a reference. But we note that there is no significant error during operations (especially during the smoothing phase of the response file). The joint use of a natural and artificial standard source is effective. Note that the calculated response can potentially process spectra far in the ultraviolet.

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3. Exploitation

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An ultimate test is to use the previously measured instrument response, as well the atmospheric transmission calculation algorithm, to calibrate the spectrum of a star near the horizon line. I selected the star HD 175892 whose reference spectrum is available in the MILES database. At the time of observation, the star was close to the meridian, at an angular elevation of only 23.7 ° (air mass of 2.48). Atmospheric absorption is therefore severe. For proof, here is the comparison between the MILES spectrum and the observed spectrum without correction of the atmospheric transmission, where one notes a very large difference:

The usual logic would be to observe a nearby reference star in the sky to evaluate a new adapted “instrument response” (a local response somehow). But we have taken care here to calculate an intrinsic response to the instrument, independent of the atmosphere transmission… The spectrum is finally reduced with the universal file “response_inst” and asking ISIS to automatically evaluate the atmospheric transmission (AOD = 0.1 and select automatic option). Here the result:

Without this being perfect (it can never be!) the calculated profile is very close to the theoretical spectrum, whereas the conditions are quite extreme (low star on the horizon). This confirms the universal nature of the calculated instrument response, and also the efficiency of the atmospheric transmission model employed, and more generally, of the processing procedure. At this point, if a significant gap were noticeable, it could be attributed to a wrong AOD choice: if necessary test a new value, which is immediate with the automatic function of ISIS, then to check if the difference is reduced (in case of doubt, it is also a technique to find at the beginning of observation for example the good ADO for the night, by observing a low star).

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Be careful concerning atmospheric differential refraction during verification and exploitation: a good result can only be obtained if the star is close to the meridian, or when the axis of the slit is oriented according to the parallactic angle, for example by a voluntary rotation of the spectrograph, or using an ADC system suitable for spectrography (see note at the beginning of the article), or modeling the effect. Of course, the problem of the differential refraction fades as we observe the stars at a high angular height compared to the horizon.

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In the acquisition conditions presented, the HD 175892 observed spectrum proves to be very well radiometrically calibrated whereas we did not need to calculate a specific instrument response for the situation, as the “response_inst” reference file could very well have been generated several weeks before the said observation. One guesses the productivity gain and the simplification of the life of the observer that this represents.

Complement. During this demonstration, I never filled the “Flat” item of the “General” tab:

What happens if we fill this item? During preprocessing, ISIS subtracts the offset, the dark, AND then divides by the specified flat-field image, for example the image “flat_2D” (see at the beginning of the article). This is a priori the “official” procedure. Ideally, it allows in particular to eliminate the shadow of dusts present in the optical path, or to correct the gain variation from pixel to pixel (this latter concerns the “high-frequency” (HF) variation of the instrument response). It is preferred here to ignore the dust traces and the PRNU (Pixel Response Non Uniformity) : it is assumed that the system is clean, free of dust – a credible hypothesis if you are careful, and that the PRNU is of low value (of the order of 1%) to make it negligible compared to other sources of response error. The problem of dividing by the “flat_2D” image is that one becomes very sensitive to the evolutions of the instrument setting, mechanical flexure and non-uniform illumination of the telescope entrance pupil (variation of the apparent F/D compared to the observation, which can change the projected position of dust shadows). If the “flat_2D” image does not coincide geometrically to the image to be processed, the cure may be worse than the harm if we want to eliminate the dust trace, for example. Also, although it is not ideal and complete, I recommend to follow rather the processing method of this demonstration, safer and faster.

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If you still want process a PRNU problem or interference fringes problem, without changing the flow presented in this article, I propose to isolate the HF component of the flat-field with a specific ISIS tool (“Masters” tab) :

Here is the characteristic aspect of the “flat_2D_HF” image thus produced:

PRNU defects are well taken into account in this new calibration image, but beware, in the parts where the flat-field image is not very intense (in the blue with a halogen lamp) the division will amplify the noise, this is a significant disadvantage. However, if you want to use such an image because your spectra are suitable or you see a big problem, do the processing by following the “pipeline” of this article, but add:

Conclusion. I presented here with some details my own procedure for reduce low and medium resolution spectrums. The end result is that the time spent finding the real response from the « long version » algorithm (better because more rigorous and necessary with UVEX) actually only represents a brief moment. The spectra acquisition and processing is greatly facilitated and the quality improved. The next step is to add a descent atmospheric chromatic correction solution for the future. In addition, unfolding this procedure (a “pipeline”) in a strict way allows to better to know his equipment and better use it eventually.

1- Introduction

UVEX is a spectrograph mainly intended for astronomical observations on relatively small sized telescopes (see detailed specifications below). Its special property is that you can manufacture it yourself, thanks to the 3D printing technology, although if you choose to build it yourself then you must also mount and adjust from scratch. The UVEX project in its current form is therefore intended for DIYers, those who want to understand the inner workings of an optical instrument, and teachers who want to offer their students a very rich, complete and motivating educational project.  Constructing and using UVEX is relevant to a number of subjects as you shift from planning to use, with the help of various physical phenomena (potentially supporting courses in physics, biology, chemistry…) and even astrophysical phenomena if the instrument is put at the end of a telescope!

You should be aware of the (moderate) risk of not reaching the end of such an adventure. And if your aspiration is rather to have a perfectly finished instrument that is immediately operational, it is better to turn to the wide ranging and high quality commercial offerings now available.

The project is presented here royalty-free for non-commercial use. Our goal is that you can complete the instrument, so here we provide information you will need for that purpose.

UVEX is a serious instrument, with which it is possible to carry out works of real scientific value. It is based on a simple configuration (essentially consisting of two mirrors) which gives it a good optical luminosity and a very wide spectral coverage, ranging from ultraviolet to infrared (depending on the camera used).  UVEX allows you to realize spectra of the visible part of the electromagnetic spectrum, but it is also worth emphasising its high efficiency in the ultraviolet, a domain almost unexplored by amateur astronomers today, and which will also interest professionals researchers. It is this feature that gives the name of UVEX, the acronym for UltraViolet EXplorer.

Here is the characteristic look of a star spectrum obtained with UVEX in the so-called “basic” configuration of the instrument (300 lines/mm grating, which is interchangeable):

This is the spectrum of the bright star Deneb obtained by mounting UVEX at the focus of a Celestron 8 telescope. Below is a detail of the violet and blue part of this spectrum showing that the detail is preserved in this area, a unusual feature in an amateur spectrographs:

But the ability to explore the infrared part of the spectrum is not forgotten, as evidenced by the two spectra of stars presented below (UVEX becomes an IREX!):

In a nutshell, UVEX is a low to medium resolution spectrograph. The resolving power R can range from R = 500 to 3500 depending on the slit width employed and the selected grating (from 300 lines/mm to 1800 lines/mm, the latter only usable for the blue part of the spectrum). As noted, both the input slit (typical width between 14 and 35 microns) and the grating are interchangeable.

UVEX is designed for use on relatively small and relatively slow telescopes. The typical instrument is a Schmidt-Cassegrain, Maksutov or Ritchey-Christian telescope of 150 to 280 mm in diameter with an aperture ratio of between F / 8 and F / 10. This is an important remark and a limitation that you must absolutely consider. If your telescope is open at F/5 (a Newton for example), UVEX is not really adapted: you will obtain a spectrum but it will be degraded (loss of resolution of 30% compared to F/10 input beam for a 25 microns slit and exploitable spectral domain reduced). An aperture at F/6 is in practice the brightest configuration usable with UVEX. Similarly, the use of a large diameter (500 mm and more) will require the use of a wide slit that automatically degrades spectral resolution performance.

The table below shows the resolving power (R) achieved at 650 nm for a telescope at F/10 and for various technical combinations offered by UVEX:

Opposite, the appearance of the solar ultraviolet spectrum according to the adopted configuration. UVEX is here mounted at the focus of a 10-inch F/8 Ritchey-Chrétien telescope that is pointed to a blue daytime sky.

UVEX has a removable camera interface. The currently designed interfaces are for ATIK cameras (see the photograph opposite) and ZWO cameras (the cooled models). For example, this spectrograph is very comfortable with a CCD camera ATIK 414EX or ATIK 460EX, or in CMOS with a camera ASI183MM pro.




The linear dimension of the spectrum usable in the plane of the detector is of the order of 13mm with a grating of 300 lines/mm and a telescope at f/10 (this would mean taking a spectral range of a little more than 4000 angstroms at one time with ASI183MM camera, for example).

The linear dimension of the spectrum usable in the plane of the detector is of the order of 13mm with a grating of 300 lines/mm and a telescope at f/10 (this would mean taking a spectral range of a little more than 4000 angstroms at one time with ASI183MM camera, for example).

A pointing/guidance device in front of the spectrograph is essential for astronomical spectrography. UVEX is compatible with the guiding cube designed for the Alpy 600 spectrograph from Shelyak Instruments. A 3D printed version of this device is also being designed in the context of the UVEX project.

For the most up-to-date information on the UVEX project, it is highly recommended to register on the ARAS forum, and to consult the section especially dedicated to the project (in addition to all the other exciting topics described in this forum, which are all invitations to observe with a spectrograph, whatever it is). We suggest you make your comments and questions on this forum.

Example of UVEX spectra

The way of optimally processing the UVEX spectra is a subject in its own right and will be the subject of other pages in the future. We suggest the reader should wait a little bit, knowing that there is already work to do if you want to make your copy of UVEX!

But while waiting, here is a set of characteristic spectra coming from this spectrograph, which give an idea of the possibilities. Note also the diversity of possible configurations. These data have a real scientific value and were acquired during the development phase of the UVEX project.

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Symbiotic stars:

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A sample of Be stars UV spectra:

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UV and blue spectrum of P Cygni star (34 Cyg) taken by using a 1200 traits/mm grating and a narrow slit (14 microns). The spectral resolution is preferred here rather than the radiometric resolution. The telescope is relatively modest, a Celestron 8:   :  

L’attribut alt de cette image est vide, son nom de fichier est spectre-uvex-6.png.

Moon spectrum (i.e. solar spectrum) near H&K Ca II lines:

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Mesure du spectre de réflectance de la planète Uranus :

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A spectral atlas

We have seen in previous sections the importance of having artificial sources of lines that produce a strong enough flux and that can be arranged facing the entrance of the telescope for adjustments. In routine use these same lamps can be used to calibrate scientific spectra in wavelength (illumination the full entrance of the telescope is best). It is recommended to have two types of inexpensive lamps: (1) a compact fluorescent lamp (but beware that legislation in Europe mean that these are disappearing, replaced by the calamitous LED lamp, but by looking hard we can still find them.), (2) a neon discharge lamp that can often be found from electrical control systems, for example.

Here are the wavelengths of the main lines that can be identified in the light produced by a compact fluorescent lamp (the fine lines come from a mercury vapor, the broad bands come from the rare earths terra deposited on the inner side of the glass bulb):

A line atlas of a neon lamp (Ne) :

For information, stellar Balmer lines, which are very useful for calibrating UVEX spectra in the ultraviolet:

5- Tuning

Tuning the Czerny-Turner is not easy, in fact this is actually the greatest difficulty for anyone who wants to embark on the UVEX adventure. The problem lies in the off-axis use of the mirrors, the large number of degrees of freedom, and the co-dependence of the effects. To illustrate this last point, an alignment defect on the mirror M1 or on the mirror M2 can have similar effects.  In this case, how do you find the correct mirror to adjust? Or, an angle error on the grating can be compensated by the orientation of the mirror M2.  It is not easy to tell when the optics are well adjusted, because aberrations can appear out of the blue. That’s the difficulty.

Do not be discouraged, because with patience we will always get it set up correctly, and finally we will be well rewarded. Here is a possible adjustment procedure…

The rule of thumb is to avoid as much as possible making settings on the telescope arranged on its mount and at night. You will exhaust yourself with little chance of a result! The correct procedure is to make all the adjustments on a table using your observing telescope (if it can be removed from its mount), or by using an auxiliary optical tube, such as a small telescope you can carry around. This bench setup is the basic work tool.  Below, a 65mm f/6.5 telescope is used as the test medium, while the spectrograph will be used on a 250mm f/8 Richey-Chrétien. This difference in size is not a problem. For optimal tuning, however, it is preferable that the test telescope was much fasty as the observation telescope.

Another essential element for the tuning is the light source. By day you can use the light from the sky, or ambient light (a white wall…) which gives for free a beautiful Fraunhofer lines spectrum of a G2V type star. A compact fluorescent lamp is also a very good companion thanks to the presence of intense mercury lines in the ultraviolet (see an atlas of lines later). For red light, it is necessary to use a neon night light. In the image opposite, we have a red night light for a child’s room in front of the objective of the telescope (not to be confused with LED sources, which emit no line)! If you find one of these lights in a store, buy it!

1. Post-tuning

The first precaution to be taken is of course to align the optical elements (M1, M2, the grating) by eye during the assembly with respect to the marks engraved in the floor of the case UV01. In this way, you should get a first spectrum on your sensor without further problems, which is a good start. But it is guaranteed not to be a very good spectrum. The orientation accuracy of the elements by eye is about 1 °, while we must achieve angle errors not exceeding 0.1 to 0.2 °.

It is recommended to use the 300 lines/mm grating to start the adjustments (the mark in the box is planned for this grating and so that the center of the visible spectrum falls in the middle of the detector when the spectrograph is well tuned, more precisely the wavelength 510-nm). You can also adjust with another grating, for example the 1200 lines/mm, but the mark will no longer be valid. For example, at the opposite, the characteristic orientation for the 1200 lines/mm grating.

Note that normally the grating change does not require a new adjustment of the entire spectrograph (mirrors M1 and M2). The operation is relatively simple: remove the UV12 support, change the grating, position the grating holder on the UVEX box, and finally, look for the orientation of the grating that makes the detector reach the part of the spectrum that we want to study. You can also decide to make a support for each diffraction grating at your disposal; it’s even faster.

2. Focus the acquisition camera

The first spectrum recorded by the electronic camera will probably be very blurred because of poor focus.  Move the camera backwards and forwards in the camera mount to make the spectrum more or less sharp (do not seek to refine it too much at this point, as the focus will be reset later after you adjust other elements of the equipment).  Ideally, the camera should be able to slide with a gentle force. If it’s too stiff, use an emery cloth on the inside of the camera mount. If the mount is too wide, attach metal tape around the body of the camera (aluminum sealing tape, try DIY stores). With practice, you will achieve a sensitivity of the order of 0.1 mm by hand adjustment. Note that a locking screw (with nut) is provided for in parts UV07 and UV08.

3. Orient the spectrum image

Next, try to align the dispersion direction and the the spectral lines with respect of the detector axis (the pixels grid). Considering the images below, the idea is to go from the top picture to the bottom picture (UVEX spectra made on a table in daylight):

Before
After

To achieve this, the camera must first be rotated in its housing in order to bring the dispersion axis parallel to the sensor lines (in the example, the presence of dust in the slit causes the accidental horizontal line, the “transversalium”, but in this case it helps to orient the camera!). It is then necessary to adjust the orientation of the slit (rotation of the piece UV04 in the UV03 housing).

Its optical design means that UVEX produces a sharp spectrum only over a relatively small slit height. UVEX is specifically designed for observing point objects, like stars (but you can also realize the spectra of small nebulae, galaxy nuclei …). A form of astigmatism occurs outside the sharp zone, which has the effect of widening the spectral lines and thus of losing spectral resolution. You can see this in the spectral image below:

… we are looking at the emission spectrum of a compact fluorescent lamp in blue. The spectrograph is correctly adjusted here, but it can be seen that the mercury lines become fuzzy at both ends of the monochromatic images of the slit. It’s a form of astigmatism. As a result, this image is really exploitable only in its central part (between the two yellow lines). Note that this area of sharpness widens as you work with slower telescope optics: it’s larger with a telescope working at F/10 than with a telescope at F/5.

Another important point to emphasize is the centering of the area of sharpness, indicated in this figure by the vertical position of the red line. Depending on the machining quality of the UV12 support of the grating, or precision positioning angle, the sharp zone can be offset upwards or downwards (or even right out of the physical width of the slit in the worst situations!). In the event of a problem, remove the UV12 support (this operation is simple, just unscrew the two screws of the UV13 lever), try to modify the inclination of the grating (possibly add a shim of paper to fix the tilting), reassemble the support, and see if the situation improves (perfect centering of the sharp area is not strictly necessary)

4. Orient the M1 miror

We now proceed to the adjustment of the mirror M1. It is here that the calm comfortable and warm bench setting makes the difference. A first approach to the adjustment is to orient the mirror M1 so that the optical beam is centered on the surface of the components that will follow (the grating, M2, the detector). For this, it is necessary to use a compact fluorescent lamp, which is successively brought to one edge, then the other, of the objective of the telescope while observing the spectrum, as in the illustrations below:

Note that the movement is on a horizontal plane. For the procedure to work it is necessary that the spectral dispersion plane is also horizontal, which involves orienting the spectrograph as shown below.

Understanding the purpose of this maneuver requires some optical principles. The following diagrams are ray tracings in UVEX belonging to an optical beam operating at F/6, with the length of the detector assumed to be about 12 mm (the grating is 300 lines/mm). First, here is the situation when the spectrograph is well tuned:

The entire the telescope pupil
is illuminated. There is no
optical vignetting (loss of
rays over the optical edges
of the components) . The
rays, however, pass very
close to the mechanical
limits (note the red part of
the spectrum that borders
the edge of the grating when
arriving at the detector).
In practice, it is necessary
to move the lamp in front
of the pupil of the telescope
during the exposure to
obtain an approximately
uniform illumination.

Here only the left edge of
the telescope mirror is
illuminated. The spectrum
is less intense, but of course,
the rays are conveyed
without vignetting from one
end to the other of the
system. Note that the
spectrum appears extremely
sharp because the beam
is very narrow, which greatly
reduces the optical aberrations
(note, this is stigmatic optics,
the physics teacher can use
this to introduce some nice
concepts of optics, and the
mathematics teacher a little
applied formalism and
geometry).  .
Now the rays come
from the only right
edge of the objective
of the telescope,
simply by moving
the light source.












Now let’s see what happens when an angle error affects the M1 mirror. In the simulation below this mirror was accidentally rotated by 1 ° (only), as indicated by the arrow:

Now the most extreme
red part of the spectrum
is vignetted by the mirror
M2 and also cut off by
the mechanical edge of
the grating. For the
observer, this corresponds
to attenuation in intensity
of the red side of the
recorded spectrum.
There is also a shift in
the wavelength range
(“green” rays no longer
reach the center of the
detector).
Illuminating the left
side of the telescope
pupil. The shift of
the spectrum is always
observed.









The case is then made
more interesting by
illuminating the right
edge of the telescope
mirror. This time the
effect of vignetting is
even more marked for
the observer.






The natural reflex in this situation is to recenter the green part of the spectrum on the detector center by orient the grating :

Turning the grating as
indicated by the arrow,
to place the green part
of the spectrum in the
center of the detector
makes everything
seem fine… …






By illuminating the left
edge of the objective,
again, we observe a
fine spectrum and in
the right place.








But the effect is spoiled
when the right edge of the
pupil is illuminated. This
time, the end of the ray
path goes past the edge
of mirror M2, and in the
image, the red part of the
spectrum is abruptly cut off.
This symptom is the sign of
a misalignment, which we
erroneously tried to
compensate for by turning
the grating, while the real
problem is the mirror M1.

Your first task is therefore to balance the vignetting on the red and blue ends of the spectrum by adjusting the orientation of M1 and using the principle of “sub-pupil” lighting. This operation is valid if the other components are at their nominal position, which is not guaranteed.  All of which means that it is then necessary to proceed by iteration, a process that requires being patient and methodical. We start here with the mirror M1 because it is more sensitive to defects.

After this first-order initial adjustment of M1, we have to work more finely by observing the inpulse response of the lines: the spot image when we illuminate the spectrograph input with a monochromatic point source (like a star that produces light only in one wavelength). An efficient way to produce a point source is to opt (possibly temporarily) for a clear slit Shelyak OP0073 or OP0092 that is mounted on the UV06 support (note, the engraved surface must be on the spectrograph side, not the telescope side, because of the presence of a chamfer). The slit system OP0073 is equipped with an isolated hole of 20 microns in diameter, the OP0092 system offers 3 aligned holes of 10, 15 and 20 microns:     

Here is the view of the spectrum of this point when using a compact fluorescent lamp: each of the points corresponds to a monochromatic image of the hole for various wavelengths (UV part of the spectrum). The telescope is working at a focal ratio of F/5:

The goal is to get an image of the point as clean and symmetrical as possible (case A). Incorrect settings of M1 preferentially generate coma (case B in the figure above). It is then necessary to retouch M1 to arrive at the case A (this is adjusted to within a few tenths of a degree).

Case C corresponds to a defect of adjustment of both mirror M1 and mirror M2 (an error on the mirror tends to widen the spectrum trace). In case D, the camera is poorly focused.

When you do not have a source hole, you have to resign yourself to examining the spectral lines, but with a less accurate diagnosis…

In the example above, the 2D spectrum of the top image corresponds to a pretty good adjustment. In the spectrum below, the group of 3 lines on the left is sharp, but the lines on the right are fuzzy, with a characteristic asymmetry of the coma.  Adjust M1 first to deal with this type of problem, while checking that the “vignetting” test has passed.

5. Orient the M2 mirror

If, when observing the source point or a star, you see the view of the spectrum below (variation of the width of the spectrum as a function of the wavelength): :

… it is necessary to rotate the mirror M2 in the correct direction to reach the result: :

6. Mongitudinal setting of the entrance slit

– if when observing the source point you can not obtain both fine spectral lines and a narrow spectrum over its entire wavelength

– if when observing a star with a telescope, the image of the slit is very sharp in the guide camera, as well as the image of the star (it appears punctual), but that the spectrum trace is hopelessly uniformly and unusually wide over its entire length (see the example below on a spectrum extract of the Arcturus star made with UVEX equipped with a network of 1200 lines / mm at the focus of a telescope opened at F / 10):

… it is likely that the planes of sharpness of the star image and focus of the cylindrical lens are not confused. This means that you can observe fine spectral details without getting a narrow spectrum, or vice versa, even when you try to focus as much as possible by moving the camera longitudinally. This is the symptom that the slit carried by the piece UV04 is not at the right distance from the mirror M1 (not respecting the 100 mm gap between the slit and M1 (see the “optical formula” section). In the part devoted to the assembly, I indicated that it was necessary to respect a distance of 1 mm approximately between the contact planes of the shoulder of UV03 and UV04.

If the anomaly of abnormally wide spectrum width appears (a spectrum wider than 15 pixels typically with 2.4 microns pixels for example), it is necessary to adjust this distance, then to redo the point of the spectrum, then finally, to note if the situation improves (in the example of the Arcturus spectrum above, the positioning error was of the order of 2 mm compared to the nominal, which means a gap slit-collimator distance of 98 mm to compare at the nominal value of 100 mm If the situation gets worse, it is necessary to move the slit longitudinally in the opposite direction.

In the opposite example, the slit support is moved so as to move the slit away from the mirror M1. In doing so, the focus point of the entire spectrograph is changed. You have to catch up by moving the camera as indicated by the arrow. This work is iterative and quite tedious because it will also at the end redo the point of the guide camera if it is already in place.

Here is the result on the image of the Arcturus spectrum as we converge towards the good result: fine lines + narrow spectrum. t.  

7. Final control

The spectrograph is correctly adjusted when, after modifying the setting for the wavelength of the spectrum (rotating the grating), the spectral lines remain sharp, see at right.

But of course the final test is on a true stellar object: all is OK if in the same time the slit image, the guide image of the star and the spectrum of the star are sharp. 



4- The assembly

The first operation is to glue the slit ring UV03 in the space provided in the UV01 housing. It is necessary to use the correct orientation, aligning the markings drawn on the front of the pieces (it is inside this ring that the slit-holder proper will be mounted, which must be correctly oriented relative to the grating grooves):

The camera interface is then mounted (in the photos below, the ZWO camera model is shown). We use a set of M4 screws and nuts for fixing:

It recommended to then mount the telescope interface, which limits the risk of later contaminating the optical components through further handling after they are installed. The interface block used here is the Alpy 600 spectrograph guide block, which can be purchased from Shelyak Instruments. This high-quality piece of metal, which is essential for good observations, is however the most expensive part of the UVEX project. A study is under way to develop as an alternative a compact module for this function, which can be produced by 3D printing and which also includes the calibration elements (spectral calibration, white lamp) and the necessary electronics. Four M4 screws are used to mount the guide box:

The slit is mounted on its support UV04 (M3 screw). The following views show the use of a Shelyak slit (in this case the model that is screen printed in a chromium layer deposited on one side of a thin glass slide): : 

A clearance of approximately 1.0 mm must be left between the contact surfaces of the UV03 and UV04 parts (this distance may be adjusted when the instrument is tuned – see next section). Note again that an adjustment in rotation makes it possible to orient the long axis of the slit parallel to the grooves of the grating. The UV05 clamp is used to complete the fixing of the slit holder.


One option is to use a “clear” slit, also part of the Alpy kit that can be provided by Shelyak Instruments. It is actually a set of slits machined into a sheet of nickel 50 microns thick. They give you a choice of slit width and a 25 microns hole, which can be a very useful artificial star during bench testing. This slits system is more economical than the model on glass and more transparent, especially in the ultraviolet, but it is also more fragile and difficult to handle. The surface is sufficiently reflective and flat to achieve good telescope guiding. The clear slit fits on the intermediate inclined support UV06 (the graved face is turner toward the mechanic support):


The next step is to mount the cylindrical lens in the housing provided in the UV01 case. The convex side should be turned towards the inside of the case.  It is very important that the installation plane of the lens is flat and well cleaned of 3D printing defects and burrs.  The longitudinal position of this component is critical in relation to the other optical components (and no adjustment is provided here, the positioning is obtained by construction).  It is not recommended to glue the lens to begin with. It is best to fix it with a quality tape, Kapton, which adheres well both on glass and on the plastic case.

The name “Kapton” is a trademark. It is a polyamide adhesive tape with remarkable mechanical, adhesive and chemical properties. It is often used in optics or to fix elements in environments as difficult as satellites. It’s easy to find this tape from merchant sites like Amazon, hardware shops or electrical hobbyist outlets. You must be careful not to dirty the optical surface during handling (if this happens, clean the glass surface by rubbing with cotton moistened with water then dry, frequently changing the cotton):

It is now time to deal with mirrors M1 and M2. They are arranged in their respective mounts (tighten the side screw gently):

The mirrors in their frames are then fixed in the support parts UV09 and UV10 (embed the FMP1 frames fully in the supports in order to line up the correct height for the optical axis):

You are now ready to mount the mirrors in the UV01 case. Note the presence of pre-positioning marks. Their appearance here is shown with white paint, to make them clearly visible:

Left, the positioning of the supports for the optical components with respect to the markings on the case.

Each of the mirror brackets is mounted with a M4 through screw. The edges of the supports are best aligned at first with respect to the position marks of the housing. The supports are equipped with a link system for fine adjustment of the mirror orientation (UV11). These elements can be moved using a screw that pulls and pushes, controlled from outside the box after slightly loosening the screw fixing the mirrors. Below is a view of these adjustment devices on the external side of the box.

Details of fine orientation tuning system of M1 and M2 mirrors: 

The last element to put in place is the diffraction grating in the UV12 support. Be careful to respect the direction of the arrow drawn by the manufacturer in relation to the support, as indicated in the photograph on the left below (the arrow gives the direction of the blaze). Also be careful to always hold the grating by the sides. Never touch the optical surface. Never rub it for cleaning. If there is dust, leave it, do not try to remove it. Tighten the M3 screw at the top of the UV12 support only quite gently (the use of a nylon screw is ideal, to avoid damaging the glass). Pass the axis of the grating support through the hole provided in the box, taking care not to put your fingers on its optical surface or that of other components – measure your gestures well. Align the support with respect to the mark drawn in the floor of UV01 (valid for a 300 lines/mm grating):

Fit the UV13 external orientation knob using the axial screw so that the rotation is relatively smooth and tighten the side screw so that the grating is well driven. During normal use of the spectrograph, you should turn this knob (slightly) to position the desired wavelength range on the sensor’s sensitive surface.

All that remains is to close the UV01 box with the UV02 cover, then slide a camera almost completely into its place in the camera mount, and you have finished construction!

3- Realisation DOWNLOAD

A view of all the mechanical parts constituting the UVEX spectrograph: : 

Files needed for 3D printing in STL format can be downloaded from the links below. The name of the nomenclature is also indicated:

UV01 : housing
UV02 : cousing cover
UV03 : slit tube
UV04 : slit support
UV05 : slit ring
UV06 : clear slit interface (optional)
UV07 : ATIK camera mount
UV08 : ZWO camera mount
UV09 : M1 support
UV10 : M2 support
UV11 : guide for M1 and M2 (2 pieces)
UV12 : grating support 
UV13 : grating position lever
UV14 : ATIK314L camera mount

It is important to be careful about choosing the material for printing. PET-G was selected for the realization of the first versions of UVEX. But it is essential to choose a material that is very opaque to light. Often the pieces look opaque to the eye, but this is not the case in the infrared.

PET-G reinforced with carbon fibres (at 20%) is a better option in terms of rigidity and opacity, but your printer must be able to use this type of wire (choice of nozzles, adjustments, etc.).

The lest image shows a plate made of material that is transparent to light in the deep red (it is lit from behind with a powerful lamp). It is almost impossible to operate an astronomical spectrograph if the structure that constitutes it is not lightproof. This is a critically important point.

If the light-tightness of the housing is still insufficient, resign yourself to covering the body of the spectrograph with one or more black cloth(s), as in the photograph below:

Experiment with the materials that suit you best, and with the slicer settings of your choice too. This is an area where everyone’s experience and mastery of their own equipment matters most.  Note in the next image the arrangement of reinforcements needed around the mounting holes of the two mirrors and the grating.

It takes about 10 hours to print the main box with a  20% density.  .

A 3D printed object is built layer by layer, each layer being deposited on the previous one. For some parts of the pieces, this “previous layer” simply does not exist, and it is therefore not possible to build the following layers in the air. Temporary support must be defined by the slicer software in these situations, which can be removed once the printing is complete. Some software automatically positions the support for you and makes suggestions. Opposite, the UVEX box with supports voluntarily added at the level of the openings, for example.

The following views show the positioning of the parts on the printer bed. All are made with a 0.2 mm layer fineness, except for the clear slit holder UV06, made with an accuracy of 0.15 mm.  If you use this piece, be careful to print it with the angled surface that receives the metal slit on the printer bed (this is the only way to have a very smooth surface). It is recommended to print the case with 3 perimeters for rigidity, while for other parts, 2 perimeters are sufficient.

A short film showing a UVEX box in progress.

A number of holes are tapped M3 and M4 (for example the holes for fixing the cover on the housing). This is a delicate operation that must be done with care. It is recommended to use the set of 3 taps in order for each diameter, and to push “rather firmly” before turning the tap holder carefully and without risking the material (only the M2 holes of the clear slit UV06 part are tapped by the screws themselves). It is necessary to push throughout the first tapping, taking care to stay as much as possible in the axis of the hole, otherwise the tap may slip. It is a good idea to train on a spare part for the first tapping.

2- The optical formula

UVEX is a spectrograph based on a relatively simple and well known Czerny-Turner design. The right figure shows the optical formula in its basic form. There are two spherical concave mirrors (M1, M2), a diffraction grating (R) to spectrally disperse the light, an input slit (F), and of course, a camera (D) to record the spectrum

In the particular case of UVEX, a cylindrical lens is added just in front of the detector to correct the astigmatism inherent in this optical formula (a cylindrical lens has a finite CURVATURE radius on an axis and an infinite curvature radius on the other axis).  The special feature of UVEX is that the design uses almost entirely mirrors, hence its property of achromatism (the absence of chromatic aberration), which allows us to observe a very wide range of wavelengths without refocusing. To preserve this achromatism, it is absolutely vital to avoid using UVEX on a telescope equipped with a focal length reducer or a field corrector. The best place is always at the direct focus of a mirror telescope (the SCT entrance corrector plate is tolerated, but absorb some UV).

More specifically, UVEX is a “crossed” Czerny-Turner spectrograph (see right figure) to facilitate the physical design (interface with the telescope and camera, compactness). As indicated above, a cylindrical lens is added, facing the detector. Its purpose is to correct the very strong astigmatism which the Czerny-Turner suffers.  Without this lens, the trace of the spectrum of the stars would be excessively wide along the spatial axis, which would greatly affect the efficiency of the instrument when observing low-brightness stars. This lens has no effect along the spectral axis (in that dimension it behaves like a simple parallel glass plate, without optical power) while along the perpendicular axis (spatial) it has a focusing effect. In the final version of UVEX (so-called Version 3), the lens is also strongly inclined relative to the average axis of the ray beam.  This design standardizes the correction of astigmatism along the spectrum – this inclination corrects the clean chromaticism of the cylindrical lens. It is made of BK7, a very transparent optical glass in the ultraviolet.


All optical elements are available from ThorLabs. The references for the order are indicated on the optical opposite drawing. Note that spherical concave mirrors are used in dedicated mounts (brackets), which are available from ThorLab. The focal length of the mirrors is 100 mm, with a diameter of 25 mm. The dimension of the cylindrical lens is 22 mmm x 20 mm.

The catalogue number in the figure is for a grating with 300 lines/mm blazed at 500 nm. The size is 25 mm x 25 mm x 6 mm.  The ThorLabs catalogue has gratings with different line densities (the maximum density usable on UVEX is 1800 lines/mm). For example, the grating of 1200l/mm blazed at 500 nm is GR25-1205, while the one blazed at 400 nm (special UV) is GR25-1204.

The slits used are those provided for the Shelyak Alpy 600 spectrograph (either printed on glass or clear slit version).

The detail of the optical scheme is given in the figures below (note: the orientation of the grating indicated corresponds to an etching density of 300 lines / mm, with the wavelength 510 nm positioned in the center of the detector):

And the following diagrams give the dimensions for the camera interfaces (for ATIK and ZWO):

Remember, since the optical elements are mostly mirrors, UVEX is not affected by chromatic aberration, the spectral range potentially covered is therefore very wide, with no need to adjust image. For example, on the ultraviolet side, the wavelength limit is the spectral cutoff induced by the Earth’s atmosphere (the ozone layer at high altitude), as shown in the figure below:

It would be necessary to go into space to do better! Another characteristic of UVEX is the high optical efficiency, which reaches 35% in the green (excluding the losses at the slit related to the enlargement of the star image because of seeing) – see the detail in the following figure:

This 35% value is a particularly high photon efficiency for a spectrograph (the final result depends on the intrinsic quantum efficiency of the detector and the wavelength). This result comes from the relatively simple optical scheme.  This is a conscious design choice, which has the tradeoff of an increase in the difficulty of adjustment compared to a more traditional spectrograph, as we will see later.