# need data-point: count rate of APD (avalanche photo-diode) for specific aperture and stellar magnitude

I hope lab / experimental physics is fair game for this web-site. If not, sorry!

I'm designing a sensor system to perform specialized [astronomy and space-sciences] experiments, and need a "reality check" to support or adjust my theoretical calculations.

What I need is the "counts per second" produced by any modern APD (avalanche photo-diode) sensor through a telescope of any specific "aperture" of a star of any "visual magnitude". I also need the number of "counts per second" of "nothing" (the "dark count") to subtract that from the "counts per second" when illuminated by the star (to determine the "counts per second" generated by the star alone).

This "reality check" will help me assure various "inefficiency allowances" I made are realistic. Examples:

#1: overall detector QE over relevant visual [and near IR] wavelengths.
#2: loss of light in atmosphere before entering telescope.
#3: loss of light in telescope optics.
#4: loss of light in fiber (if any).
#5: anything/everything else.


As implied, I am only interested in the APD operating in "photon counting mode" (not analog).

I've read about 5 dozen articles that discuss APDs for astronomy, but none give a straightforward value. The closest I found was a vague statement that the limited magnitude was 22nd magnitude on a 6-meter telescope based upon observations of the crab nebula pulsar. But this is not specific and the object is highly variable (on a short time frame). They did not say, for example, whether they consider their "limiting magnitude" is where the count rate rises from 200 per second (dark count) to 220 per second (measurement), or 200cps to 400cps, or over what time period, or any other indication of their definition.

All I need is ONE clear statement of cps for any aperture and visual magnitude star. You'd think I could find that in dozens if not hundreds of articles, but... no. Probably a clear statement like I need exists in some article somewhere, but I haven't seen one. Have you? Or better yet, have you made such an observation yourself?

The following detail is not very important (but just to be complete), my primary applications perform fairly high time-resolution measures on fairly bright stars. In other words, the experiments generally need to measure in the range of "counts per microsecond" to "counts per millisecond". Typically APDs max out at around 15 to 50 million counts per second, and most of my experiments will be working at 10K to 10M counts per second to observe the short time-period phenomenon I need to measure.

• The difficulty (or at least one difficulty) is that you are asking for a convolution of photons per second per unit area time the area element of your detector times the quantum efficiency of the detector weighted over the spectral distribution of the light. Any serious treatment will consider those as three different thing to compute, leaving the trivial detail of multiplication to you. – dmckee Mar 16 '14 at 2:15
• Also, you get the dark rate in general by reading the data sheet for your device and you get the actual dark rate by measuring it (i.e. you put the cover on the scape and take a dark frame). – dmckee Mar 16 '14 at 2:17
• @dmckee: The area of the sensor is not relevant as long as the entire star image falls on the sensitive part of the APD (though dark count tends to be higher on larger area sensors). I can get QE versus wavelength from the sensor datasheet, and the spectral curve of the star from the star identity. Nonetheless, I'm not naive enough to imagine the resulting precision can be super high, since atmospheric clarity varies from night-to-night and hour-to-hour at any land-based observatory. Yes, I know how to measure dark noise and read datasheets! But hopefully they measured their dark noise! – honestann Mar 16 '14 at 3:47
• @dmckee: One reason THEIR dark-count is helpful is because dark-count is very temperature dependent. Even if they don't have a cooled sensor, the temperature in an instrument on a telescope in the outdoors can vary from -50C to +50C... or more. – honestann Mar 16 '14 at 3:55