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One of the most important choice that you will have to make when designing your spectrometer is to select the proper sensor for light detection. For reasons that extends way beyond this post, I am a huge fan of Machine Visions cameras for that kind application and I will urge you to throw away your linear CCD detectors (Sony ILX511 or whatever you are currently using). I promise that I will make a post to justify that in the future but for now on you will have to trust me: cameras are the way to go for the amateur spectroscopist.

The problem with cameras is that they come in all flavours and shapes and it can be intimidating to select one at first. In this post, I would like to address the choice of a camera for spectroscopy in a scientific way such that we can optimize our choice based on quantitative data.

To select the best cameras that could be recommended for spectroscopy I have started by listing all the cameras available at PointGrey with all their documented performance characteristics. I chose PointGrey because, to my knowledge, they offer the largest documented database about their cameras.

From an initial list to this day of 248 cameras, I have kept only 60 entries by removing colour cameras, cameras with incomplete or suspicious data (so goodbye GS3-U3-14S5M-C with its 5400 seconds exposure time). By the way, you do not want to use colour camera for spectroscopy because that will just ruin your performances due to the Bayer filter. Use only monochrome ones and don’t even think about using a webcam.

I then started thinking on a way to order the remaining list to sum up all the data into a performance figure. This was however not possible because it depends too much on your application, like how much resolution you need for what spectral range and so on. There is, however, one invariant that we can accept in all cases:

**“We never have enough photons in a spectroscope”**

and that is all that matters in the end.

From that observation I have drawn two major parameters of the system:

1. For a given spectral range and resolution, we would like the slit to be as large as possible to allow the maximum amount of light to enter the spectrometer.

2. For a given irradiance (W/m²) on the sensor, we want the noise to be as low as possible to detect small signals.

Because the size of the slit is directly linked to the size of the sensor (see in [»] this post why), we therefore want to have the largest sensor possible. That means optimizing for the product of the number of pixels and size of the pixels.

The second factor is a bit more difficult to express. From the EMVA 1288 standard, I developed the following formula which is a good approximation to the signal-to-noise level in low light conditions:

where p is the pixel size, t_{max} the maximum integration time allowed by the camera, σ_{d,0} the temporal dark noise of the camera at zero integration time in e^{-}, µ_{I} the read-out-noise in e^{-}/s and η the quantum efficiency.

The formula is actually relatively easy to interpret. For a given irradiance, the signal will be proportional to the surface irradiated and the exposure time multiplied by a conversion factor, the quantum efficiency which says how much electrons are generated per photons that hit the sensor. Cameras with large pixels, long exposure time and high quantum efficiencies will therefore be favoured. The denominator is the noise in the system. Noise will grow with the photon noise and the thermal electron noise. Because we are in low-light conditions however, the photon noise will be considered to be much smaller than the thermal electron noise and can therefore be neglected. The variance of the remaining thermal noise can be expressed as growing linearly with the integration time. Cameras with low temporal dark noise and low read-out noise will therefore be favoured too.

We see here that time plays a mixed role because long exposures will bring more photons but also more thermal electrons. However, it is always good to have larger exposure times as the numerator will always grow more quickly than the denominator in our equation.

I unfortunately ran into a problem when trying to compute this figure of merit because PointGrey does not give both the temporal dark noise and the read-out-noise. There seems to be some confusion there but I cannot understand why they do not deliver both values. They do however give other data that can be useful to us.

To overcome this issue, I have used the following formula that approximates the previous one:

It uses µ_{p} the absolute sensitivity threshold which is the number of photons required to reach a SNR or 1. To alleviate the behaviour of time in the previous equation, I considered the worst case and made the benefits of time goes as with its square root only. Note that the quantum efficiency has disappeared from the formula as it is already hidden into µ_{p}.

From these two criteria (sensor size and low-light performances), I made the plot of Figure 1. Cameras were split into three price colour groups (<500 EUR, <=1250 EUR and >1250 EUR) for easiness of reading. All prices are given ex-VAT.

I further pruned the list of cameras by selecting only the *dominating* entries. An entry is said to be dominating if it *dominates* all other values. And because this is so far a definition loop, a value is said to be dominated if there exist any other entry which has all its criteria better or equal to the value being dominated. So, for instance, the camera BFS-U3-04S2M-CS is a dominator because there exists no camera that has better detectivity. Camera BFLY-PGE-23S6M-C is also a dominator because there exists no camera that is at least as good in both its sensitivity __and__ its sensor size in its price category.

I have annotated the dominators in Figure 1 with the camera name. Some of these cameras are available in both their GiGE (PGE) versions or their USB3 (U3) version. The final list therefore contains only five cameras that ought to be examined: the BFS-PGE/U3-04S2M-CS, the BFLY-PGE-23S6M-C, the GS3-U3-91S6M, the GS3-U3-123S6M-C and the GS3-U3-89S6M-C.

The cameras BFS-PGE/U3-04S2M-CS are two low cost cameras sold 285 EUR for the PGE version and 305 EUR for the U3 version. They are both designed around the Sony IMX287 sensor which has a low absolute sensitivity threshold of 6.57 photons with large pixels of 6.9 µm which is relatively rare considering that it is a CMOS and not a CCD sensor. The only downside of that cameras is that the sensor is relatively small with only 720×540 pixels. Following the [»] dispersion over resolution guideline, this sensor would only be recommended for applications with a limited number of bands to be resolved, ideally less than 240. Put differently, if you would like to image a band of 400 nm, you should not set the resolution below 1.7 nm with that sensor. Among the other parameters, the camera has a maximum acquisition time of 30 seconds and a well capacity of about 22000 electrons. At full well capacity, this would yield a SNR of 149:1 per expositions.

If you would like to have more bands imaged and not lose too much sensitivity at roughly the same price, I would recommend moving to the BFLY-PGE-23S6M-C cameras. This camera is sold 379 EUR and is based on the Sony IMX249 CMOS sensor. Although it features a smaller pixel size of 5.86 µm (which is still huge compared to other CMOS sensors), it has an absolute sensitivity threshold of 9.45 photons. This is not as low as the BFLY-PGE-04S2M-CS and the pixel size are a bit smaller, but the camera features an impressive resolution of 1920×1200 pixels. That basically allows 640 bands to be imaged which is 2.5 times what the BFLY-PGE-04S2M-CS could do. Based on my recent experience with spectrometers, it is unlikely that you manage to build a good spectrometer with such a massive resolution unless you throw away all of your étendue. The camera also has a maximum integration time of 32 seconds and a well capacity of about 33000 electrons yielding a potential SNR of 182:1 per expositions. I have however to give a warning with this entry because, for some reason, PointGrey website list a 32 seconds max exposition time for the PGE version but only a 3.9 seconds max exposition for the U3 version. I don’t know if this is an error or not and I will contact them to try to find out. If that were to be an error, it would change a little bit the domination ordering but would still be a very good camera in terms of sensor size at reasonably good low-light performances.

If for some reason 640 bands is not enough for your applications, you can select either the GS3-U3-123S6M-C (4096×3000) or the GS3-U3-89S6M-C (4096×2160). These cameras are however horribly expensive with prices well above the 2000 EUR. If you absolutely need more bands than the BFLY-PGE-23S6M-C, that you don’t want to pay the price of these cameras and you are ready to throw away some detection performance, you can select the GS3-U3-91S4M-C which has a 3376×2704 sensor for about 1000 EUR.

Considering that the average spectroscopist does not have thousands of euros to spend into a camera, I would therefore recommend either the BFS-PGE/U3-04S2M-CS or the BFLY-PGE-23S6M-C depending on the spectral range and resolution that you would like to achieve. Most of the time, however, you may be interested in having a jack-of-all-trade that can give you more resolution for about the same sensitivity and the BFLY-PGE-23S6M-C is therefore the way to go if you plan to buy only one camera for all your experiments.

If you already have a BFLY-PGE-23S6M-C, don’t hesitate to contact me to share your impressions on that camera!

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