Abstract

The principles and concepts of a wave-front analyzer based on spot edge scanning techniques and rising and falling illuminance slope comparisons are reviewed. An analyzer implementing these techniques and designed to be used with an adaptive optics element for the real time correction of low order aberrations is described. An evaluation of the tilt output channels of the analyzer shows a linear operating range exceeding ±500 μrad, frequency response exceeding 250 Hz, and a noise equivalent tilt angle of 4 μrad. For the focus and astigmatism channels, the analyzer output is linear over an ∼2.5–3-μm range of aberration input for a diffraction-limited (DL) spot. The instrument gain falls from ∼8.5 V/μm for a 1 × DL spot to ∼4 V/μm for a 6 × DL spot. The noise equivalent aberration increases from 0.025 μm for a 1 × DL spot to ∼0.05 μm for a 6 × DL spot.

© 1983 Optical Society of America

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References

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  1. R. Barakat, A. Houston, J. Opt. Soc. Am. 54, 768 (1964).
    [CrossRef]
  2. B. Tatian, J. Opt. Soc. Am. 55, 1014 (1965).
  3. D. Holmes et al., Air Force Weapons Laboratory Technical Report AFWL-TR-76-268 (1977).
  4. R. Barakat, A. Houston, J. Opt. Soc. Am. 53, 1244 (1963).
    [CrossRef]
  5. C. Neufeld et al., AFWL TR-81-72 (1982), Vol. 1, contract F29601-77-C-0062.
  6. A. Erteza, Appl. Opt., 15, 877 (1976).
    [CrossRef] [PubMed]
  7. J. Nichols, D. Duneman, Opt. Eng. 22, 366 (1983).
    [CrossRef]

1983 (1)

J. Nichols, D. Duneman, Opt. Eng. 22, 366 (1983).
[CrossRef]

1976 (1)

1965 (1)

1964 (1)

1963 (1)

Barakat, R.

Duneman, D.

J. Nichols, D. Duneman, Opt. Eng. 22, 366 (1983).
[CrossRef]

Erteza, A.

Holmes, D.

D. Holmes et al., Air Force Weapons Laboratory Technical Report AFWL-TR-76-268 (1977).

Houston, A.

Neufeld, C.

C. Neufeld et al., AFWL TR-81-72 (1982), Vol. 1, contract F29601-77-C-0062.

Nichols, J.

J. Nichols, D. Duneman, Opt. Eng. 22, 366 (1983).
[CrossRef]

Tatian, B.

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Opt. Eng. (1)

J. Nichols, D. Duneman, Opt. Eng. 22, 366 (1983).
[CrossRef]

Other (2)

C. Neufeld et al., AFWL TR-81-72 (1982), Vol. 1, contract F29601-77-C-0062.

D. Holmes et al., Air Force Weapons Laboratory Technical Report AFWL-TR-76-268 (1977).

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Figures (10)

Fig. 1
Fig. 1

Detector layout sketch and channel voltage output dependence on aberration components.

Fig. 2
Fig. 2

Scanning wave-front analyzer.

Fig. 3
Fig. 3

Optical schematic of analyzer.

Fig. 4
Fig. 4

Laboratory optical layout.

Fig. 5
Fig. 5

Tilt channel static response.

Fig. 6
Fig. 6

Focus P4 channel response to defocus aberration: (a) 0.076-; (b) 0.159-; (c) 0.318-; (d) 0.476-cm source.

Fig. 7
Fig. 7

Astigmatism P5 channel response to P5 aberration: (a) 0.076-; (b) 0.159-; (c) 0.318-; (d) 0.476-cm source.

Fig. 8
Fig. 8

Astigmatism P6 channel response to P6 aberration: (a) 0.076-; (b) 0.159-; (c) 0.318-; (d) 0.476-cm source.

Fig. 9
Fig. 9

Analyzer gain variation with source diameter.

Fig. 10
Fig. 10

NEAb vs source diameter.

Tables (3)

Tables Icon

Table I Focus P4 Channel Response Parameters

Tables Icon

Table II Astigmatism P5 Channel Response Parameters

Tables Icon

Table III Astigmatism P6 Channel Response Parameters

Equations (12)

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I = I 0 2 π σ 2 exp ( x 2 / 2 σ 2 ) .
I = I 1 2 π σ 2 exp ( x 2 / 2 σ 2 ) ,
I 1 I 0 = exp [ ( 2 π N λ ) 2 ] ,
d I d x max = 0.24 I 1 σ 2 .
d I d x = 0.084 I 0 σ 2 .
d I d x wheel 1 = 0.24 σ 2 I 0 exp [ ( 2 π × 0.264 ) 2 ] = 0.015 I 0 σ 2 ,
d I d x wheel 2 = 0.24 σ 2 I 0 exp [ ( 2 π × 0.064 ) 2 ] = 0.204 I 0 σ 2 .
P 4 = 1 2 k 4 ( V 0 + V 90 ) ; P 5 = 1 2 k 5 ( V 0 V 90 ) ; P 6 = 1 k 6 [ ½ ( V 0 + V 90 ) V 45 ] .
A = ( d 2 s d t 2 ) 2 d t ,
A = ( Δ 2 ERF Δ T 2 ) 2 d t ( Δ 2 ERF Δ T 2 ) 2 d t leading edge or trailing edge or ahead of focus behind focus
NETA = ( V noise / G ) .
NEAb = ( V noise / gain )

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