ME770; Fall 2007; Prof. Sanders; Homework #3; Due Oct 8, 2007

You are to assess the low-light capabilities of a camera based on this chip:

http://homepages.cae.wisc.edu/~ssanders/me_770/product_datasheets_and_manufacturer_data/Micron_CMOS_camera_on_chip_JBG.pdf

How many megapixels is this camera?

As background, we need to understand light levels. We know that outside on a sunny day it is ‘bright’ and outside at night it is ‘pretty dark’, but we need to put numbers on this. The max irradiance outside on a sunny summer day, high noon, is around 1 kW/m2. Let’s put the sun at a 45 degree angle, something like 4:30 pm in the summer. Then let’s assume the irradiance drops to 707 W/m2 (this is a Sanders estimate, feel free to improve it by talking to people that understand solar stuff if you like, and let Sanders know what you find). Then let’s imaging you are filming a vertical object like a standing person, with your back to the sun, so the person you are filming is looking at you and squinting because the sun is behind you. The person is at a 45 degree angle to the incoming light, so the intercepted irradiance is 500 W/m2 of their area (we are now a factor of 2 below what we started at). The incoming sunlight is well collimated (you can find the divergence knowing only the diameter of the sun and the distance to the sun), but the person scatters this collimated radiation into 2π Sr. Let’s assume the person also absorbs 50% of the light. So we are now looking at an object radiating 250 W/m2 into 2π Sr. This is broadband. We only care about the visible part. So you must use the blackbody calculator (http://infrared.als.lbl.gov/calculators/bb2001.html), modeling the sun as a 5800 K blackbody, to figure out how much light the camera actually sees. Furthermore, the camera collects less than 2π Sr of the radiated light, and this must be taken into consideration. These ideas are summarized in sheet one of http://homepages.cae.wisc.edu/~ssanders/me_770/homework_assignments/HW_3_calculations_ME770_fall_2007.xls

We will consider the above case (4:30 pm on a sunny summer day) to be the baseline case, and we’ll call it ‘one sun’. We are interested, in this assignment, in low light levels, so fractions of ‘one sun’. One additional reference point of interest is the irradiance due to a full moon. If we assume the moon also receives 1 kW/m^2, and that the spatial arrangement is moon--Earth------sun, we can estimate that ‘one moon’ is about 5x10-6 suns as detailed on sheet 2 of

http://homepages.cae.wisc.edu/~ssanders/me_770/homework_assignments/HW_3_calculations_ME770_fall_2007.xls


So we now have enough information to calculate powers incident on our camera and to relate them to familiar situations like full sunlight and full moonlight. Now we need to understand the SNR of the Micron camera as a function of

parameter / minimum value / maximum value
object illuminating irradiance (I) / 5e-6 suns / 1 sun
camera temperature (T) / -50 C / +70 Cm-1
frames per second (fps) / 2.22 / 30
distance between object and videocamera (L) / 1m / 30m
size of object (D) / 0.3m / 10m
lens diameter (d) / 0.003m / 0.1m

The SNR you calculate should not be based on this line from the datasheet:

unless you can figure out what that is.

Instead, you should develop a spreadsheet (or other computer code) to calculate SNR vs. I, T, fps, L, D, and d in their given ranges. Plot some sample results by fixing 4 or 5 of the parameters and plotting versus the remaining 1-2. Your analysis should include

·  dark noise (for T dependence, extrapolate the value from the Micron datasheet according to the trends given in Prof. Ghandhi’s slides)

·  read noise (for fps dependence, extrapolate the value from the Micron datasheet according to the trends given in Prof. Ghandhi’s slides)

·  bit noise

·  shot noise

You should assume the maximum acceptance angle of each camera pixel is 10 degrees (half angle).

After you finish with your spreadsheet / code and make a couple representative plots, select a system that might be practical for a consumer to buy (cooling that can be achieved without carrying around a liquid nitrogen dewar, a reasonable size lens, etc.) and estimate the lowest light level (in fractional suns) for which you expect satisfactory video results to be obtained.