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SAPPHIRE  HOMOGENEITY
Following are homogeneity phase maps of the first 25 x 10 cm sapphire substrate measured at Caltech.  These maps show the central 150 mm of the first 250 mm sample.  Uncertainty is ~5nm due to turbulence.

If low order terms (Seidels) are subtracted (a compensating polish scenario) the following are the residual Peak to Valley and rms.
 
Terms Analysis:
Terms removed  PV(nm) RMS(nm)  
Tilt 444  66  
Tilt, Power 453  59  PSD
T,P, Astigmatism 431  55  
T,P,A, Coma 449  53  
T,P,A,C, Spherical abberation 409 51 PSD

A note about PSDs...
Shown are X and Y average PSDs,  we can compare initial LIGO fused silica with Sapphire using the same software... whether this software gives the correct absolute amplitude values is still under investigation. 12-27-00

AFTER HOMOGENEITY COMPENSATION AT GOODRICH
FIRST POLISH - 14.6nm rms. Side 1 through bulk, reflect off side 2.  No manipulation
 
 

FUSED SILICA HOMOGENEITY - FOR COMPARISON
2ITM04 Homogeneity  PV=77 nm,  rms=10 nm      2ITM04 PSD   (both have Tilt and Power subtracted)
Taken at CSIRO, this map shows the central 150 mm of the full aperture phase map

Other LIGO 1 Fused Silica
CSIRO measurements of 15cm sapphire