L. Furey, T. Dubos, D. Hansen, and J. Samuels-Schwartz, "Hubble Space Telescope primary-mirror characterization by measurement of the reflective null corrector," Appl. Opt. 32, 1703-1714 (1993)
The reflective null corrector used to manufacture of the Hubble Space Telescope contains valuable information about the prescription of the primary mirror since an excellent null was achieved between the null-corrector wave front and the primary-mirror wave front. During the Phase I measurements, the leading cause of the spherical aberration, the field lens position error, was discovered and remeasured to an accuracy of ±0.005 mm. To derive the conic constant of the primary mirror to an accuracy of ±0.0003, we remeasured the parameters of the reflective null corrector that could contribute to the spherical aberration of the primary mirror.
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Measured Radius-of-Curvature Values for the Calibration Mirror, NM1, and NM2a
Uncompensated Radius (mm)
Temperature (°F)
Pressure (Hg)
Humidity (%)
N
C
Compensated Radius (mm)
Calibration mirror
350.6512
71.7
29.59
30
266.4862
0.9997336
350.5578
350.6513
70.7
29.60
30
267.0924
0.9997330
350.5577
350.6511
70.6
29.60
30
267.1441
0.9997329
350.5575
350.6515
70.6
29.60
30
267.1441
0.9997329
350.5579
350.6516
70.6
29.59
30
267.0537
0.9997330
350.5580
Average
350.5577
Sigma
0.0002
NM1
286.7436
71.2
29.30
31
264.1149
0.9997360
286.6679
286.7432
71.3
29.30
31
264.0638
0.9997360
286.6675
286.7432
71.7
29.30
31
263.8595
0.9997362
286.6676
286.7430
71.6
29.30
31
263.9105
0.9997362
286.6673
Average
286.6675
Sigma
0.0002
NM2
372.9292
70.7
29.43
33
265.5503
0.9997345
372.8302
372.9290
70.9
29.43
33
265.4474
0.9997346
372.8300
372.9293
70.8
29.43
33
265.4731
0.9997346
372.8303
372.9286
70.7
29.43
33
265.5246
0.9997345
372.8296
372.9289
70.9
29.43
33
265.4474
0.9997346
372.8299
Average
372.8300
Sigma
0.0002
The equations used to calculate the environmental compensation effect of the measurement are described fully in the HP 5527A manual (App. E, Wavelength-of-Light Compensation). The equations are
where C is the compensation factor and
where T is the air temperatures (in degrees Fahrenheit), P is the air pressure (in inches of mercury), and H is the humidity (%).
Table 2
Zernike Polynomials Orthogonalized Over an Annular Aperture Radius of Central Obscuration of 0.3300
Summary of Conic-Constant Values After Phase I and Phase II Measurements
Measurements
Derived Primary-Mirror Conic Constant
Derived Primary-Mirror Conic Constant Error Bars
Zernike P11 rms Wave Front with 0.33 Obscuration
λ = 0.6328 μm
μm
Phase I (FLPE only)
−1.01345
−0.0007 to +0.0006
−0.4012
−0.2539
Phase II (All data)
−1.01377
±0.00014
−0.4129
−0.2613
Tables (5)
Table 1
Measured Radius-of-Curvature Values for the Calibration Mirror, NM1, and NM2a
Uncompensated Radius (mm)
Temperature (°F)
Pressure (Hg)
Humidity (%)
N
C
Compensated Radius (mm)
Calibration mirror
350.6512
71.7
29.59
30
266.4862
0.9997336
350.5578
350.6513
70.7
29.60
30
267.0924
0.9997330
350.5577
350.6511
70.6
29.60
30
267.1441
0.9997329
350.5575
350.6515
70.6
29.60
30
267.1441
0.9997329
350.5579
350.6516
70.6
29.59
30
267.0537
0.9997330
350.5580
Average
350.5577
Sigma
0.0002
NM1
286.7436
71.2
29.30
31
264.1149
0.9997360
286.6679
286.7432
71.3
29.30
31
264.0638
0.9997360
286.6675
286.7432
71.7
29.30
31
263.8595
0.9997362
286.6676
286.7430
71.6
29.30
31
263.9105
0.9997362
286.6673
Average
286.6675
Sigma
0.0002
NM2
372.9292
70.7
29.43
33
265.5503
0.9997345
372.8302
372.9290
70.9
29.43
33
265.4474
0.9997346
372.8300
372.9293
70.8
29.43
33
265.4731
0.9997346
372.8303
372.9286
70.7
29.43
33
265.5246
0.9997345
372.8296
372.9289
70.9
29.43
33
265.4474
0.9997346
372.8299
Average
372.8300
Sigma
0.0002
The equations used to calculate the environmental compensation effect of the measurement are described fully in the HP 5527A manual (App. E, Wavelength-of-Light Compensation). The equations are
where C is the compensation factor and
where T is the air temperatures (in degrees Fahrenheit), P is the air pressure (in inches of mercury), and H is the humidity (%).
Table 2
Zernike Polynomials Orthogonalized Over an Annular Aperture Radius of Central Obscuration of 0.3300