# Using SNAP itself to span many magnitudes

#### Michael Richmond Sep 19, 2002

Suppose that SNAP can observe a 14th magnitude star without saturating. Does that mean that we can use SNAP itself to transfer the calibration from a 14th magnitude star to a 25th magnitude supernova?

Let's look at the process. Consider two stars: A, at V=14, and B, at V=25. Star B is the "target": a supernova at z=1, near maximum light. Star A is the "calibrator": a bright star, perhaps a white dwarf, with known fluxes and/or colors across the visible and IR.

```                              0.4*(25-11)
ratio of intensity = 10             =  25,000
```

In the collaboration meeting in Feb, 2002, Bebek discussed observational strategies for both visible and IR detectors. He suggested combining exposures of length 200 seconds in sets of 4 to reach the faint limit. According to my notes, the visible detectors will have

```            QE = 60%
dark current 0.02 e-/sec/pix
0.1 arcsec per pixel
```
I've made a few reasonable assumptions and calculated the signal from star B which we would receive in a combined 800-second exposure: roughly 1000 electrons within an aperture of radius 4 pixels. The signal-to-noise ratio for this exposure is roughly 25, meaning that the random uncertainty in the brightness of star B will be around 0.04 mag.

Can we simply change the exposure time to 1 second, look at bright star A, and compare the two signals to derive the magnitude of star B? Let's see: in a 1-second exposure with FWHM = 2 pixels, star A will produce roughly 32,000 electrons inside the aperture. Roughly 40 percent of this, or 13,000 electrons, will appear in the central pixel. If the full well capacity is 60,000 electrons (as quoted by Mike Lampton, http://costard.lbl.gov/Snap/get/Calibration/113/1.html) then this sounds reasonable.

But consider

1. shutter timing
2. dark current
3. cosmic rays
4. flatfielding

shutter timing
In order to avoid a systematic error of 1% between the bright star A and faint star B, the ratio of the exposure times must be accurate to 1 percent. One way to do this is to ensure that both the long and short exposure times are accurate to within 1 percent each. For the faint star B, with individual exposure time of 200 seconds, this isn't hard. But for the bright star, A, we must open and close the shutter for exactly 1.00 seconds, with a maximum error of plus or minus 0.01 seconds. Can the SNAP shutter move that quickly and that precisely?

If not, then we introduce a systematic error to all observations of faint SNe.

dark current
The short exposure lasts for 1 second. If the dark current is 0.02 e-/sec/pix, then any individual pixel is likely to have no electrons knocked free at all by thermal motions during the exposure. Fine and good.

But the 200-second exposures are likely to accumulate an average of 4 electrons in each pixel. This is fraction of the signal from the faint target star B (at least in the central pixels of the PSF). Measuring the dark current accurately enough to subtract it is probably not hard. That's good, too.

In the infrared, however, this may be more difficult.

cosmic rays
The short exposure lasts for 1 second. During this period, the chance that a cosmic ray strikes any particular pixel is very small.

But the 200-second exposures are likely to accumulate many cosmic rays. One of the reasons to take multiple 200-second exposures instead of a single longer exposure is to reject cosmic rays.

If the cosmic-ray rejection is not done properly, then measurements of faint objects in long-exposure frames will be biased in some manner. This is a possible source of systematic error between short and long exposures.

flatfielding
The short exposure of bright star A will place its light in just a very few pixels on a single chip.

If we have the luxury of orienting the spacecraft so that the single faint star B falls on exactly the same pixels, we avoid flatfielding errors entirely.

However, this isn't going to happen. The SNAP spacecraft will not be able to orient itself specially for each SN. Instead, SNe will fall randomly on chips across the entire focal plane. Unless the large-scale flatfielding across the entire focal plane is accurate to 1 percent, we risk adding systematic errors to the bright/faint comparison. Note that if the location of star A on the focal plane happens to be a maximum or minimum of sensitivity, then ALL SN measurements will be in error, systematically; averaging together SNe which fall in different locations will not help.