# Electron count rates in SNAP images

#### Michael Richmond Apr 15, 2004

In order to make realistic simulations of the signal and noise in SNAP images, I have been trying to figure out the rate at which photons from the sky and from stars will strike our detectors, and the rate at which electrons will be knocked free by dark current. My goal isn't to do a perfect job, but be within a factor of 20 or 30 percent of the true numbers. That will suffice for my testing purposes.

Since others may be interested in the same quantities, I list them here. If I've made an error, please let me know so that I can fix these pages.

I assume the following:

```         Sky background for SNAP

SNAP     central   width    photons per
filter   waveln    (Ang)    sq. arcsec
index    (Ang)              per sec
----------------------------------------------------------------
0      4753       974       65
1      5513      1130       88
2      6396      1311       94
3      7419      1521      112
4      8606      1764      134
5      9983      2046      129

6     11580      2374      104
7     13433      2754      101
8     15582      3194       91
--------------------------------------------------------------
```

How many photons does SNAP collect from a star which has magnitude zero in each passband? I calculated this at three wavelengths (roughly 5500, 8000, 12500 Angstroms, corresponding to V, I, J passbands), and then simply made a linear fit to number of photons per second versus filter index. It should be within a factor of 25 percent, I would estimate. The linear fit is:

``` photons per sq.cm. per sec =  1,225,000  -  122,600*(filter_index)
```

Here are the numbers for each passband.

```    Approximate magnitude zeropoint for SNAP

SNAP     central   width    photons per
filter   waveln    (Ang)    sec for star
index    (Ang)              of mag = 0
----------------------------------------------------------------
0      4753       974       3.84e10
1      5513      1130       3.46e10
2      6396      1311       3.08e10
3      7419      1521       2.69e10
4      8606      1764       2.31e10
5      9983      2046       1.92e10

6     11580      2374       1.54e10
7     13433      2754       1.15e10
8     15582      3194       0.77e10
--------------------------------------------------------------
```

What about the background due to the instruments? We can break this up into readout noise (fixed) and dark current (increases with time). I grabbed these numbers from Chris Bebek's presentation on the camera, dated 2/8/2002. I treat the properties of the chips as uniform within each of the two wavelength ranges. Chris Bebek provided a value for the dark current of the visible CCD chips, but it was so small that I've treated it as zero.

```                      visible               IR
------------------------------------------------------------
quantum efficiency      80%                70%

dark current             0 e-/pix/sec       0.05 e-/pix/sec

------------------------------------------------------------
```

One needs some additional information to add up the number of photons or electrons which will contaminate the measurement of a single star. I assume that a reasonable aperture to use for measuring the light has a radius of about three times the FWHM.

```                      visible               IR
------------------------------------------------------------
pixel size (arcsec)      0.1                0.12

FWHM (arcsec)            0.14               0.14

(arcsec)

number of pixels        55                  38
in aperture
------------------------------------------------------------
```

Putting all this together, a quick first pass at the signal-to-noise ratio for stars of magnitude 20 with the standard 4x300-second exposure set turns out to be:

```SNAP filter index      signal          S/N
(electrons)
---------------------------------------------------------
0                   368,640         580
1                   332,160         540
2                   295,680         503
3                   258,240         458
4                   221,760         410
5                   184,320         367

6                   129,360         305
7                    96,600         253
8                    64,680         196
---------------------------------------------------------
```