Throughput of MEMS generated SLIT as a function of Dither Positions

Fourier Optics Analysis

March 26, 2002
First, we assume an ideal PSF for a circular telescope aperture with a 15% central obscuration.

figure 1: assumed pupil figure 2: PSF superimposed on MEMS generated slit, logarithmic scale.

figure 3: slit throughput as a function of dither position.
figure 4: total throughput (= slit + aperture stop, 20% oversizing) as a function of dither position. With 20% oversizing, diffraction losses are a significant effect.
Figure 5: histogram of throughputs at random position within slit. The black curve are the computations which takes into account only the geometrical effect of the PSF on the MEMS generated slit. The red curve is for the same computation but including the diffraction effects. Note that losses by diffraction are largest at positions where the slit throughput is already small.
The above calculation is a worst case scenario since it uses an overly optimistic PSF. More realistic PSFs should include at least some aberration and a more realistic pupil function. The same calculations as above were carried out using a segmented mirror and some support structure as the pupil function.

Figure 6: possible NGST pupil. (J. Krist)

a) b) c) d)

Figure 7: used NGST PSFs plotted with log scale:
a) circular mirror, 15% obscuration (same as figure 2)
b) same as a, but aberration with total rms wavefront error of 0.2mu
c) segmented mirror as shown in figure 6
d) same as c, but aberration with total rms wavefront error of 0.1mu

Figure 8: histogram of throughputs at random position within slit for the PSF shown in figure 7c. The black curve are the computations which takes into account only the geometrical effect of the PSF on the MEMS generated slit. The red curve is for the same computation but including the diffraction effects.
Relative contribution of diffraction for the different PSFs. The loss from diffraction depends on the dither position and varies between about 10% and about 50%. The mean diffraction loss is computed as
1-(mean total throughput)/(mean throughput at slit).

The number of random dither positions needed to obtain a flux accuracy of 10% by averaging the measured fluxes is computed as

n_dither= (3*rms / mean /0.1)^2
where rms and mean are the rms and mean value of the throughput (including diffraction) from a grid of dither positions.
PSFdiffraction loss n_dither
a)19.7%64
b)18.8%9
c)19.6%36
d)18.9%24
Figure 9: Strehl ratios of the PSFs as a function of wavelength.