Confocal Spectrometric Telescope

In today’s post, I revisit my old setup of [»] confocal spectroscopy by creating an add-on for our [»] 350-700 nm spectrometer that allows sampling a point on a remote scene to analyze its spectral content. I will discuss in more detail how the system was designed, how it can be reproduced, and give some experimental results obtained with it as well as a spectral calibration procedure. As usual, all the CAD files can be downloaded [∞] here for reproduction under a CERN OHL V2 license.

A sketch of the system is given in Figure 1 where you can spot a color camera (top left), a fiber port to probe the scene (bottom left), and a 100 mm achromat lens with an aperture in front of it to acquire the scene (bottom right). The fiber port must be mounted on a XY mount to allow centering of the probe position such that we sample the scene exactly at the center of the camera sensor. This allows easier operation because you can turn on the crosshair inside the viewing camera software to know exactly where you will sample the scene. Here, I’m using a 50 µm fiber directly connected to the spectrometer so the spectral resolution will be 1.0 nm and the sampling area will be 1.7’ large (0.028°).

The optical layout of our add-on is fairly simple and consists of only a 100 mm achromat and a beam-splitter cube. The system is shown in Figure 2 along with its optical performances. It performs not as good as the raw doublet due to the presence of aberrations introduced by the thick cube beam-splitter as explained [»] here.

The exact position of the cube does not matter (see [»] here why) but it was important to dimension the aperture properly to achieve sufficient image quality. After some trial and error, I came up with an aperture of 15 mm which was a good trade-off between light collection and optical quality. It is important to keep the aperture as small as possible to achieve good image quality, but at the same time to keep it large enough to collect light from the scene. Indeed, for a point-source, the amount of light intercepted will be

with X the coupling efficiency, d the distance between the object and the observer and D the diameter of the aperture.

Increasing the aperture diameter can be done by either complexifying the optical design and keeping the focal length constant (decrease in f-number), or by keeping the f-number constant and increasing the focal length accordingly. Increasing the focal length is an easier choice because we can still use standard achromatic doublets, but it unfortunately has the effect of decreasing the FOV and sampling area which can make object tracking more difficult to achieve. As an example, upgrading the design with a 500 mm focal length achromat would allow gaining a factor 25 in coupling efficiency but will decrease the sampling area to 20” (5× less).

Here, I opted for a 100 mm f/7 design but we will see later that it limits us for dim objects.

With the 15 mm pinhole, you can see in Figure 2 that the performances at the center are relatively correct despite some large chromatic aberrations in the blue region. This will have other consequences that I will cover below. The performances remain acceptable at 70% of the FOV but drops quickly at the edge of the sensor. This is not necessarily an issue because we will primarily use the center of the sensor and use the complete image only to locate the object into the scene more easily.

Assembly is done without much difficulty as per Figure 3. The front lens is aligned first by projecting a cross on the camera sensor using an [»] autocollimator, and the fiber port focus is aligned second by projecting some light from the fiber to the autocollimator.

The XY alignment procedure for the fiber port is a bit more generic than the one presented in our [»] former post and is shown in Figure 4. A relay system is assembled, and a crosshair is projected on the telescope using an autocollimator. The autocollimator crosshair is centered on the center of the telescope camera, using the camera software provided by the supplier and by enabling the crosshair overlay. Using the alignment camera, the fiber port is adjusted in XY until the fiber lays at the center of the autocollimator crosshair. This was harder than expected because Thorlabs C1XYA part isn’t very stiff, and it was pretty easy to screw up the alignment by bending a bit the cage system. I would therefore advise against using a fiber smaller than 50 µm with this setup unless this problem is mitigated.

To achieve the best performance, two achromat of f=75 mm separated by a 9 mm aperture of were selected. The performances of the relay system is given in Figure 5 for a LED light source centered at 625±25 nm, such as the one we use in our autocollimator setup. The performances are diffraction limited on a 2 mm diameter disk. The relay system of Figure 5 is relatively generic and can be re-used for visualization through a 25 mm cube, such as when aligning our [»] autocollimator.

Figure 6 shows the final assembly of our telescope add-on which features an extra baseplate to attach the telescope on an equatorial mount for easier star tracking, and a mirror mounted on a kinematic cage base for finer adjustments of the objects on the scene. The baseplate was designed for my own equatorial mount (a Paralux 114-900 mount) and you might need to adapt it if your equatorial mount has different fixtures holes positions.

Some initial results are shown in Figure 7 where I aimed the telescope on an outdoor scene and sampled both some copper oxide and leaves. Despite they share similar colors, we can spot differences in their spectra.

When I generated the spectra of Figure 7, I was initially surprised to see that they were shifted towards the blue region of the spectra – thus distorting the reproduced color patch to a blueish color.

Analysis of Figure 2 reveals the origin of the issue. Because of the strong chromatic aberrations of the telescope system, the blue region of the spectra is coupled differently than the green and red regions. Depending on how you set up your focus alignment, you may either favor the blue region or the green-red region. Adding the quantum efficiency of the sensor and the transmission properties of optical components (lenses, cube and fiber optics), the sampled spectrum does not match the actual color of the object under analysis. Note that I did not observe such strong differences in the former setups ([»] absorbance and [»] fluorescence add-ons), so it’s likely that the chromatic focal shift of our telescope system is the primary contributor to the trend observed here.

Calibrating a spectrometer is a relatively complex task but we can already get close enough by using a standardized source and comparing the measured spectrum to the expected one. It can be hard (or just expensive) to get a calibrated standardized source, but Thorlabs QTH10 Quartz-Halogen source should be pretty close to a blackbody of T=2800 K for which we can compute the expected response as

with λ, the wavelength in nanometers, h, Planck constant (6.62607015×10^-34 m²kg/s), k_B, Boltzmann constant (1.380649×10^-23 m²kg/s²K), c, the speed of light (299,792,458 m/s), and, T, the temperature in Kelvin.

The curve s(λ) needs to be normalized, either at the wavelength of peak intensity, or at some arbitrary wavelength:

with λ_r the reference wavelength of your choice.

If you wish to normalize at the peak wavelength, it depends on temperature through the Wien’s law:

At T=2800 K, we expect the maximum to occur at 1,035 nm, outside of the spectrometer operating range. This is not an issue as we only need numbers within a reasonable range to get rid of the very large exponents that have no real meaning.

Figure 8 shows the experimental measurement of the QTH10 lamp along with the expected blackbody response and the same QTH10 spectrum but corrected using a polynomial calibration curve factor (see below).

From an experimental spectrum and its expected response, we can compute a calibration law, c(λ), by taking the ratio between the two at each wavelength. Since we expect this calibration law to be smooth due to the origins of the mismatches which vary themselves smoothly with wavelength, a polynomial fit is usually a good approach.

The calibration curve along with its polynomial fit is given in Figure 9. I increased the order of the polynomial until the agreement with the data was good enough as to provide a R²>0.99. Note that the calibration curve shall be used only within the range of measured data, as the polynomial may diverge strongly outside of this range (as can be seen in Figure 9 for wavelengths below 350 nm and above 700 nm). Also, I did not display the equation of the polynomial here because it depends on your particular setup. More specifically, the calibration curve will change every time you refocus the telescope due to the chromatic aberration coupling issue I mentioned earlier.

As an illustration of what can be achieved with this telescope add-on, I aimed the setup at a LED streetlamp 100 meters away. The results can be seen in Figure 10. The increase in noise in the red region is due to the calibration curve of Figure 9 which clearly favors the blue light with a tenfold difference between 700 nm and 400 nm. Note that the color patch in Figure 10 is not 100% accurate because the results were taken with a former integration of the system, before I computed a calibration curve. The focus was probably slightly different at that time, resulting in a different chromatic coupling. Nonetheless, it is good enough for our demonstration here.

I also decided to aim the telescope at the sky to acquire a spectrum of sunlight diffusion in the atmosphere. The results are shown in Figure 11 and we can spot Balmer’s hydrogen lines at 410 nm, 434 nm, 486 nm and 656 nm. For the historical note, it is from these lines that [∞] Cecilia Payne proved in her PhD thesis in 1925 that the sun was composed mainly of hydrogen gas. Beware that although the spectrum of Figure 11 looks noisy, it isn’t. The noisy appearance is actually due to the many absorption lines of the earth’s atmosphere, in addition to the emission lines of the sun. The spectrometer resolution is unfortunately too coarse to resolve them properly for a chemical analysis of the sun and the atmosphere.

Extending the results of Figure 11, I tried to acquire a spectrum of the star [∞] Betelgeuse with its characteristic orange color in the winter night sky. The results are shown in Figure 12 but are unfortunately too noisy to derive any reliable analysis. We could hypothesize that we spot its Iron peak at 516 nm and its titanium oxide peak at 545 nm but it’s really difficult to judge due to the very low light levels achieved here, especially in the red region of the spectrum where noise clearly dominates. Figure 12 is a good illustration of the limitations of the system due to the limited size of the aperture. Using a telescope such as the AP 80/480 ED Triplet Photoline OTA from TS OPTICS would result in a signal increase of about 10×, alleviating this issue. Also, the results of Figure 12 were strongly limited by my limited tracking ability with my unmotorized equatorial mount and I couldn’t achieve more than a few second exposure without even getting the star centered on the probe properly most of the time. This phenomenon would be even more exaggerated with the TS OPTICS telescope because of its longer focal length and a high-quality tracker would be needed for sure. That being said, despite I would have loved to perform this experiment deeper, I couldn’t afford the price of a telescope and a motorized equatorial mount…

Last but not least, the telescope add-on of Figure 1 can be used in very different scenarios as well! Because it is an infinity-conjugated telescope, we can easily turn it into a microscope by placing a microscopy objective in front of it. Figure 13 illustrates this by showing a close-up on a neon bulb. I will not develop this example further because it’s going to be the topic of my next article!

To summarize, we have seen in this post how to create a telescope add-on for our spectrometer and showed some of its design and performance. We emphasized the importance of aperture selection as well as the impact of the chromatic aberrations on the acquired spectra and proposed an easy calibration method to compensate the effect. We then illustrated some of the example usages of the telescope by showing the analysis of remote objects (leaves, rust, and streetlamp) and showed its limitations with an analysis of the spectrum of the star Betelgeuse. We concluded by showing how versatile the add-on is by turning it into a microscope setup to take a spectrum of a specific location of a neon bulb emission.

It is worth noting that we used here our 350-700 nm spectrometer but since the add-on is fiber coupled, it is possible to connect it to any type of spectrometer provided it works in the VIS region. Extending to UV or NIR would be possible, provided the different optical elements (lens, cube beamsplitter and fiber) are adapted in consequence.

In the next post, we will continue investigating the usage of the add-on in microscopy systems! So be sure to stay tuned in for updates :)

I would also like to give a big thanks to Young, Sebastian, Alex, Stephen, Lilith, James, Jesse, Jon, Cory, Karel, Sivaraman, Samy, David, Michael, Shaun, Themulticaster, Kausban, Tayyab, Kirk, Marcel, Onur, Dennis,  Benjamin,  Sunanda,  M and Natan who have supported this post through [∞] Patreon. I also take the occasion to invite you to donate through Patreon, even as little as $1. I cannot stress it more, you can really help me to post more content and make more experiments!