Optical Characterization of the ACIS UV/Optical Blocking Filters.

Measurements of the optical transmission of a multilayer filter composed of Al/Polyimide/Al = 330Å/2000Å/330Å at PSU (values of multilayer thicknesses reported by LUXEL corporation) were used to constrain the optical constants for polyimide. To infer the real and imaginary parts of the refractive index from the transmission measurements we constructed a model transmission function with optical constants for polyimide parameterized as:

$$n(\lambda) = A + B/(C - \lambda)$$

$$k(\lambda) = D + E/(F - \lambda)$$

where n and k are the real and imaginary parts of the refractive index for polyimide.

The optical transmission of the ACIS multilayer filters was calculated using the matrix method described in Born and Wolf, 1980. By solving Maxwell's equations for the total electric and magnetic field with boundary conditions at the filter interfaces one finds that the relation between the incident and exiting electromagnetic fields can be written in matrix notation as :

$$\left( \begin{array} {c} {\rm E}_{I} \\ {\rm H}_{I} \\ \en... ...rray} {c} {\rm E}_{II} \\ {\rm H}_{II} \\ \end{array} \right)$$ (46)

$$\rm M ~=~ \left\vert \begin{array} {c c} \cos(k_0) & i \sin(... ...} \\ Y_{1} i \sin(k_0) & \cos(k_0) \\ \end{array} \right\vert$$ (47)

where M is the characteristic matrix of the stratified medium.

A least squares fit of a model transmission function, incorporating the above parameterization of n and k, to the measured optical transmission data provided the optical constants for polyimide which were then used to predict the the optical transmission performance of the flight filters. In Figure 5.6 we present a fit of our model transmission function to the polyimide data.

 

Figure 5.6: A fit of an optical transmission model to measured optical transmission of an aluminized polyimide sample. 

Figure 5.7 shows the real part of the refractive index for polyimide resulting from the fit of our model to the optical transmission data for the polyimide sample.

 

Figure 5.7: Real part of refractive index for polyimide. 

We incorporated the derived optical constants of polyimide into a transmission model for the ACIS-I and ACIS-S flight multilayer filters. For the simulations of the ACIS I and S transmissions we assumed the following thicknesses:
ACIS-I : Al/Polyimide/Al = 1200Å/2000Å/400Å
ACIS-S : Al/Polyimide/Al = 1000Å/2000Å/300Å

Figure 5.8 and Figure 5.9 show the prediced optical transmission of the ACIS-I and ACIS-S OBF's respectively. Peaks appear in the transmittance, one at about 4300 Å and the other at about 8500 Å. The two peaks in the transmission curve shift toward smaller wavelengths as the incident photon angle is increased.

The amplitude of the transmission does not change significantly in the 3-7 degree range (the angle of incidence of rays at the HRMA focal point is expected to range from 3 to 7 degrees), however, for large incident angles (> 60 degrees) the transmission at 8000 Å is expected to increase by about one order of magnitude (with respect to the normal incidence case). This effect may need to be considered especially if a large scattered optical light component is present.

 

Figure 5.8: Predicted Optical Transmission for the ACIS I OBF for angles between photon direction and normal to CCD of 0, 30 and 60$\deg$.  

 

Figure 5.9: Predicted Optical Transmission for the ACIS S OBF for angles between photon direction and normal to CCD of 0, 30 and 60$\deg$. 

The diffuse transmission through the ACIS UV/Optical filters was calculated using the expression:

$$T_{diff}(\lambda)=\frac{\sum(w(\theta_{n-1},\theta_{n})*T(\theta_{n-1},\theta_{n},\lambda))}{\sum(w(\theta_{n-1},\theta_{n}))}$$ (48)

where $w(\theta_{n-1},\theta_{n}) = cos(\theta_{n-1}) - cos(\theta_{n})$, is a weighting function that takes into account the differential solid angle that the filter `sees' for incident photon angles between $\theta_{n}$ and $\theta_{n-1}$.

$T(\theta_{n-1},\theta_{n},\lambda)$ is the transmission for rays incident at an angle of $\theta_{n-1}$.$T(\theta_{n-1},\theta_{n},\lambda)$ was calculated for incident angles of 0,1,2,...89 degrees. Figure 5.10 and Figure 5.11 show the predicted transmission including interference effects for diffuse light for the ACIS I and S OBF's respectively.

 

Figure 5.10: Predicted Optical transmission for the ACIS I OBF for diffuse illumination.  

 

Figure 5.11: Predicted Optical transmission for the ACIS S OBF for diffuse illumination.