# Status Report for Oct 22, 2003

One task for the Calibration Team is to decide on a strategy for the initial observations to be made during the "commissioning phase" of the mission, during the first few months after launch. Some of these observations will require special modes of observing. We must figure out exactly what needs to be done so that the mission planners can accomodate our needs.

#### How many different photometric effects might there be?

Lots. This is not an exhaustive list.

1. each chip has a different zero point
2. each filter+chip combination has a slightly different intrinsic bandpass
3. each filter+chip combination is struck by light at a different incidence angle
4. each chip has intrinsic variations in sensitivity across its face
5. the entire focal plane may have variations in illumination

#### How can we correct for each effect?

We need information -- lots of information. Watch as we build up an equation which includes terms for each of the above effects.

Consider the conversion of an instrumental magnitude m to its equivalent M on some standard system. With a perfect single detector, one would simply make a single shift:

```          M   =   m   +  a
```
where a is a zero-point offset term.

However, there are 72 different chips in the SNAP focal plane, which makes the equation

```          M   =   m   +  a
i
```
where a_i is the zero point for chip i.

If the instrumental bandpass doesn't match the standard bandpass exactly, then there will be small corrections which depend on the color of the star.

```          M   =   m   +  a    +  b  * (color)
i       j
```
where b_j is the first-order color term for a particular chip+filter, and color is some measure of the star's color. Note that we measure color with SNAP by observing the same star on two different filter+chip detectors, so this implies that the telescope must point in slightly different directions so that stars move from one filter+chip to another.

But the effective bandpass will shift slightly across each chip+detector, because the angle of incidence will change. We may need to take this into account, in which case we would need to replace the single color term with a more complicated expression:

```          M   =   m   +  a    +  b1  * (color)  +  b2  * theta * (color)
i        j                 j
```
where we now have a constant b1 and a slope b2 term for each chip+detector, and theta is the angle of incidence at which light strikes the detector.

If the sensitivity of each chip is not perfectly uniform across its face, then we need to correct for this "small-scale" flatfielding error. We might approximate the changes in sensitivity as a low-order polynomial function p of (row, col) position on the chip.

```          M   =   m   +  a    +  b1  * (color)  +  b2  * theta * (color)
i        j                 j

2
+  p1  * row   +  p2  * row    +
i              i

2
+  p3  * col   +  p4  * col    +
i              i

```

There might be variations in illumination across the entire SNAP focal plane which could also be characterized reasonably well as a low-order polynomial function q of (x, y) position on the focal plane.

```          M   =   m   +  a    +  b1  * (color)  +  b2  * theta * (color)
i        j                 j

2
+  p1  * row   +  p2  * row    +
i              i

2
+  p3  * col   +  p4  * col    +
i              i

2
+  q1  * x     +  q2  * x      +

2
+  q3  * y     +  q4  * y

```

How many coefficients are there in this very simple strawman model?

```          72     chip zero points
180     color "intercept" terms
180     color "slope" terms
4*72     small-scale (chip) flatfield coefficients
4     large-scale (focal plane) flatfield coefficients
--------
724     coefficients

```

#### How can we determine all these coefficients?

The answer is simple, in theory: observe a field of stars over and over and over, slewing the telescope slightly from one picture to the next. As stars move small distances across each chip, we get information on the small-scale flatfield terms. As they jump to another chip+filter combination, we get information on their colors, and can solve for the color-dependent terms. As they move from one chip to the next, we get information on the zero-point terms. As they move long distances across the focal plane, we get information on the large-scale flatfield coefficients.

Short exposures will suffice. There are a hundreds of stars over the entire focal plane in a single very short exposure with the right magnitude to give high signal-to-noise measurements. The real questions are:

• Exactly how should we slew the telescope from one image to the next?
• How many exposures will it take to determine each coefficient to a satisfactory level of confidence?

In order to answer these questions, we can run simulations in which we "acquire" images of stars (with all the photometric effects in place), then run the measurements through a big least-squares fitter to determine the values of the coefficients. By comparing the known input values to the least-squares output values, we can estimate the uncertainty which remains after any proposed sequence of images.

#### What first?

Using the simple SNAP simulator I have built, I am starting small: investigating the number of exposures required to determine the zero-point terms a_i only, given detectors which are otherwise perfect and perfectly known.