Abstract

We demonstrate a method for testing optics (spherical and aspheric) and other reflecting or transmitting objects. We call this experimental ray tracing. A laser beam is sent through the sample, and its propagation is determined with a lateral effect photodiode. A modified Hartmann test can be performed by measurement of beam location within two planes. Measurement in one plane close to the focus delivers a spot diagram. The method is well suited for testing even strong aspheric optics. As a further use we demonstrate 3-D shape measurement of nonplanar glass plates, e.g., car windshields.

© 1988 Optical Society of America

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References

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  1. J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenk. 24, 1 (1904).
  2. A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).
  3. H. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer Generated Hologramms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).
  4. K. Andresen, B. Morche, “Digitale Verarbeitung von Kreuzrasterstrukturen zur Verformungsmessung von Flächen,” VDI Ber. (Ver. Dtsch. Ing.) 480, 19 (1983).

1983 (1)

K. Andresen, B. Morche, “Digitale Verarbeitung von Kreuzrasterstrukturen zur Verformungsmessung von Flächen,” VDI Ber. (Ver. Dtsch. Ing.) 480, 19 (1983).

1980 (1)

H. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer Generated Hologramms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

1972 (1)

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

1904 (1)

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenk. 24, 1 (1904).

Andresen, K.

K. Andresen, B. Morche, “Digitale Verarbeitung von Kreuzrasterstrukturen zur Verformungsmessung von Flächen,” VDI Ber. (Ver. Dtsch. Ing.) 480, 19 (1983).

Fercher, A. F.

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

Hartmann, J.

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenk. 24, 1 (1904).

Kriese, M.

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

Morche, B.

K. Andresen, B. Morche, “Digitale Verarbeitung von Kreuzrasterstrukturen zur Verformungsmessung von Flächen,” VDI Ber. (Ver. Dtsch. Ing.) 480, 19 (1983).

Tiziani, H.

H. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer Generated Hologramms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

Optik (1)

A. F. Fercher, M. Kriese, “Binäre synthetische Hologramme zur Prüfung asphärischer optischer Elemente,” Optik 35, 168 (1972).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer Generated Hologramms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

VDI Ber. (Ver. Dtsch. Ing.) (1)

K. Andresen, B. Morche, “Digitale Verarbeitung von Kreuzrasterstrukturen zur Verformungsmessung von Flächen,” VDI Ber. (Ver. Dtsch. Ing.) 480, 19 (1983).

Z. Instrumentenk. (1)

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenk. 24, 1 (1904).

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Figures (14)

Fig. 1
Fig. 1

Basic principle of the Hartmann test.

Fig. 2
Fig. 2

Experimental setup for a modified Hartmann test using a PSD.

Fig. 3
Fig. 3

Reconstructed rays propagating near the focus of an achromat.

Fig. 4
Fig. 4

Reconstructed rays propagating near the focus of an achromat. The achromat is slightly tilted against the optical axis.

Fig. 5
Fig. 5

Experimental setup for measuring the local refraction of aspheric optics.

Fig. 6
Fig. 6

Position signal of the PSD vs location x of the transmitting beam in the pupil plane for an aspheric spectacle lens with small errors.

Fig. 7
Fig. 7

Position signal of the PSD vs location x of the transmitting beam in the pupil plane for an aspheric spectacle lens with large errors.

Fig. 8
Fig. 8

Geometry for calculating the local refraction of aspheric optics from PSD data.

Fig. 9
Fig. 9

Local refracting power vs location x of the transmitting beam in the pupil plane: (1) achromat f = 800 mm, (2) aspheric spectacle lens with small errors.

Fig. 10
Fig. 10

Local refracting power vs location x of the transmitting beam in the pupil plane of an aspheric spectacle lens with large errors.

Fig. 11
Fig. 11

Geometry for calculating the shape of a nonplanar glass plate from the measured beam displacement.

Fig. 12
Fig. 12

Experimental setup for measuring the shape of a nonplanar glass plate.

Fig. 13
Fig. 13

Results of two measurements of the beam displacement across the same line on a car windshield. The detector was moved laterally by ~50 μm between measurements 1 and 2.

Fig. 14
Fig. 14

Calculated screen shape from the data of Fig. 13 using Eq. (11). The calculated shapes of measurements 1 and 2 are plotted on top of each other to demonstrate repeatability. The differences are within the linewidth of the plot.

Equations (11)

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p ^ ( x ) = x + γ · [ p ( x ) - p 0 ] ,
p ^ ( x 1 ) = x 1 + γ 1 · [ p ( x 1 ) - p 0 ] ,
p ^ ( x 2 ) = x 2 + γ · [ p ( x 2 ) - p 0 ] ,
Δ p ^ ( x 1 , x 2 ) = p ^ ( x 2 ) - p ^ ( x 1 ) ,
Δ p ^ ( x 1 , x 2 ) = Δ x + γ · Δ p ( x 1 , x 2 ) .
f ( x 1 , x 2 ) = - z · Δ x γ · Δ p ( x 1 , x 2 ) .
D ( x 1 + ½ Δ x ) = 1 f ( x 1 , x 2 ) = - γ · Δ p ( x 1 , x 2 ) z · Δ x .
δ D ( δ p ) = [ ( D p 1 δ p ) 2 + ( D p 2 δ p ) 2 ] 1 / 2 = 2 · γ z · Δ x δ p .
V ( φ , n , D ) D φ ( 1 - 1 n ) ,
z ( x ) = z 0 + 0 x φ ( x ) d x = z 0 + n D ( n + 1 ) 0 x V ( x ) d x .
z ( x N ) = z ( x 0 ) + n D ( n - 1 ) i = 1 N V ( x i ) · ( x i - x i - 1 ) .

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