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I’m attempting to build a spectrometer and I’m having difficulty assessing the performance of a particular sensor. I am a novice and other posts on this forum have helped me greatly but I still haven’t been able to arrive at an answer that makes sense. I’d appreciate any help in identifying where I am going wrong. My goal is to assess my photon budget by determining:

  1. the sensor sensitivity in units of enter image description here,
  2. the pixel well depth (full well depth) in enter image description here, and
  3. ultimately the sensitivity in enter image description here.

Most sensors I’ve been looking at make it easy enough to calculate this (if I’m doing it right) but for various reasons I’m looking at trying to make the ThorLabs CCS200 work for this application. The datasheet for the sensor, Toshiba TCD1304DG, does not give the chip’s pixel well depth and only offers sensor sensitivity in [V/(lx∙s)]. I’ve found another site, Avantes, that reports the pixel well depth and sensitivity for this chip in [photons/count] but when I try to calculate these values I end up with wildly different answers that I have little confidence in.

Here is the path I’ve been taking (assuming the incoming photon has a wavelength λ = 600 [nm]):

Knowns for the TCD1304DG chip (from the datasheet) and the CCS200 system:

  • Sensitivity: 160 [V/(lx∙s)] (page 3)
  • Pixel Saturation: 0.600 [V] (page 3)
  • Pixel Size: 8 x 200 [μm^2 ] = 1.6E-9 [m^2 ] (page 1)
  • Quantum Efficiency: 0.96 [e^-/photon] (at 600 [nm], graph on page 10) (EDIT, not actually Q.E. as pointed out by user1850479)
  • Resolution: 16 [bit] (ADC on CCS200 webpage)

Attempted Conversions:

Starting with sensitivity, the conversion from lux to lumen flux is straight forward: [lx]=[lm/m^2 ]. Lumen to watt is much more frustrating for a physics application. Assuming a perfectly narrow band of light at λ = 600 [nm] the conversion from lumen to Watt looks like either η = 431 [lm/W] for a Photopic conversion, or η = 56 [lm/W] for a Scotopic conversion (Luminous Efficacy Tables). I don’t know which type of conversion to use for this application (neither result in an answer consistent with the values given on the Avantes site). I’ll assume Photopic conversion for this post. That leads to:

enter image description here

So the equivalent sensitivity is 160 [V/(lx∙s)] ∙ 431 [lm/W] = 68,960 [(V∙m^2)/J] (which is equivalent to [V/((W∙s)/m^2)]).

The energy of a photon at λ = 600 [nm] is 3.31E-19 [J/photon]. Given the pixel size, the sensitivity becomes:

68,960 [(V∙m^2)/J] ∙ 3.31E-19 [J/photon] ∙ 1/0.95 [photon/e^-] ∙ 1/1.6E-9 [pixel/m^2] = 1.502E-5 [(V∙pixel)/e^-]

With a saturation voltage of 0.600 [V], the full well depth becomes:

0.600 [V] ∙ 1/1.502E-5 [e^-/(V∙pixel)] = 39,947 [e^-/pixel]

For comparison, Avante states the full well depth as 120,000 [e^-/pixel]. I’m off by a factor of 3.

Given an ADC with 16 bit resolution, the change in voltage per count on a given pixel is: 0.600/2^16 = 9.155E-6 [(V∙pixel)/count]

That leads me to a photon per count of: 1/1.502E-5 [e^-/(V∙pixel)]∙ 1/0.95 [photon/e^- ]∙ 9.155E-6 [(V∙pixel)/count]= 0.642 [photon/count]. That doesn’t make sense. Again for comparison, Avante states the sensitivity as 60 [photon/count]. I’m off by two orders of magnitude.

There is something fundamental here that I don’t understand. Any guidance would be greatly appreciated and could help others attempting to analyze similar photon budgets.

UNITS: [ V/((W∙s)/m^2) ], [ V/((W\$\ast\$s)/m^2) ], [ e^- ], [ photons/count ], [ V/(lx∙s) ], [ V/(lx\$\ast\$s) ], [ V/lx\$\ast\$s ], [ lx ], [ lm/m^2 ], [ nm ], [ lm/W ], [ e^-/pixel ]

SCREENSHOTS: enter image description here
CCD Chip

enter image description here
Compact CCD Spectrometer Summary Specs

enter image description here
Avantes Assessment of Detector Specs

EDITED: To improve readability and to include screenshots of highlights in certain links.

user3338262
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1 Answers1

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I don't think that CCD includes an ADC, so the volts/count you see in different products are specific to the analog gain and ADC chip used in that specific product. Hence the numbers you calculate won't agree with numbers for other products.

As for why that datasheet is incredibly evasive about basic sensor properties such as sensitivity and quantum efficiency, that is because that is an extremely low end sensor from the early 2000s. It is meant for applications were you have enough light that sensitivity isn't important. The fact that you're trying to do these calculations suggests that this part is not appropriate for your application.

If you want a CCD as opposed to something more modern, I would look at the hamamatsu catalog. They have reasonable datasheets and you can call them up and ask questions.

user1850479
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  • Thank you user1850479 and I agree, it looks like Thorlabs is selling this as a very low-end system for simple bread board applications. Both the Thorlabs link and the Avante link I cite state that they're using 16 bit ADC... so in theory (unless I'm missing something) the predicted performance should align. The CCD spec sheet does give the Q.E. from on page 10 of their datasheet. It looks like I didn't enter the link correctly. I'll edit this post to include screenshots for better readability. – user3338262 Nov 30 '19 at 02:42
  • I've used that Thorlabs spectrometer for 6 or 7 years. It's fine for what it's meant to do, but it is not meant for low light measurements. Using a 16 bit ADC doesn't mean the gains are the same. The figure on page 10 is not the QE, but it is made to look like it. – user1850479 Nov 30 '19 at 02:51
  • Ah good to know. Thanks for the first hand knowledge, user1850479. I'm looking for a signal in the 1 [uW] range. I'd assume this falls into your definition of "low light", correct? Two followup questions: 1) do you have a system you would recommend for this or is it better to just breadboard the whole thing? 2) assume that I did actually have the correct Q.E., ADC resolution, etc., did I apply the rest of the conversion correctly above or am I still missing something fundamental or simple? EDIT: grammar – user3338262 Nov 30 '19 at 03:29
  • For more clairity: 1[uW] non-uniformly distributed over a 110 [nm] range in wavelength. – user3338262 Nov 30 '19 at 03:42
  • 1 uW over what integration time? Over 1 second, that will be about 1 billion photons per pixel which is an extremely strong signal. That Thorlabs spectrometer might work there, although the high dark current is a problem for long integration. I think your logic was right above, although CCDs were before my time so I could be mistaken. If you can breadboard it and buy a modern CMOS camera that will give you the best sensitivity. To put into perspective, sensitivity on that CCD is probably about 50-100 photons, modern sensors are 3-10. – user1850479 Nov 30 '19 at 03:45
  • Interesting. My integration time is 0.004 to 0.060 [s]. For my target wavelength that'll get me something like 4.5 million photons per pixel. Dark current will be less of a problem at those frame rates and I have other DSP methods for dealing with noise... if I can get the signal digitized in the first place. – user3338262 Nov 30 '19 at 04:02