Abstract

We propose a high-speed, parallel system for lens aberration measurement employing a confocal optical setup. This method uses a non-interferometric, conventional confocal axial response to determine the spherical aberration coefficient of a confocal objective. The aberration coefficients are successfully calculated from the intensity axial response by employing a neural network. It is estimated that the system can find out the aberration coefficients of 10,000 microlenses in 20 seconds of measurement and 1 second of calculation time. Our experimental results also demonstrate the practicality of this system.

© 2002 Optical Society of America

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References

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Appl. Opt. (3)

J. Microscopy (1)

T. Wilson and A. R. Carlini, �??The E.ect of Aberrations on the Axial Response of Confocal Imaging System,�?? J. Microscopy 154 243�??256 (1989).
[CrossRef]

J. Mod. Opt. (3)

H. J. Matthews and D. K. Hamilton and C. J. R. Sheppard, �??Aberration Measurement by Confocal Interferometry,�?? J. Mod. Opt. 36, 233�??250 (1989).
[CrossRef]

H. Zhouand M. Guand C. J. R. Sheppard, �??Investigation of Aberration Measurement in Confocal Microscopy,�?? J. Mod. Opt. 42, 627�??638 (1995).
[CrossRef]

H. Zhouand C. J. R. Sheppard, �??Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,�?? J. Mod. Opt. 44, 1553�??1561 (1997).
[CrossRef]

Nature (1)

D. E. Rumelhart and G. E. Hinton and R. J. Williams, �??Learning representation by backpropagation errors,�?? Nature 323, 583�??586 (1986).
[CrossRef]

Opt. and Laser Eng. (1)

H. J. Tiziani and T. Haist and S. Reuter, �??Optical inspection and characterization of microoptics using confocal microscopy,�?? Opt. and Laser Eng. 36, 403�??415 (2001).
[CrossRef]

Opt. Eng. (3)

Tae-Seok Yang and Jun Ho Oh, �??Identification of primary aberrations on a lateral shearing interferogram of optical components using neural network,�?? Opt. Eng. 40, 2771�??2779 (2001).
[CrossRef]

Joseph M. Geary and Phil Peterson, �??Spherical aberration: a possible new measurement technique,�?? Opt. Eng. 25 286�??291 (1986).

Qian Gong and Smiley S. Hsu, �??Aberration measurement using axial intensity,�?? Opt. Eng. 33 1176�??1186 (1994).
[CrossRef]

Opt. Lett. (1)

Other (1)

Developed at University of Stuttgart, Maintained at University of Tubingen, �??Stuttgart Neural Network Simulator,�?? <a href="http://www-ra.informatik.uni-tuebingen.de/SNNS/">http://www-ra.informatik.uni-tuebingen.de/SNNS/</a>.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the confocal setup employed to measure the axial intensity response, where FT lens is a Fourier transform lens, Mag. lens is a magnification lens, and BS is a beam splitter. The pupils of the microlenses are imaged on the CCD camera, and the reference mirror is driven axially by a stepping motor. The response includes the aberration information of the objective. (b) One example of axial intensity response.

Fig. 2.
Fig. 2.

The schema of a neural network for determining aberration coefficient from confocal intensity-axial-response.

Fig. 3.
Fig. 3.

Estimated spherical aberration coefficients. The lateral axis and the height axis respectively represent designed aberration coefficients and estimated coefficients. ×, ∗, and o respectively denote the results from trained, untrained, and experimental axial responses. The solid line represents an ideal estimation.

Fig. 4.
Fig. 4.

The learning curve of the neural network. The learning process can clearly be classified into four processes.

Fig. 5.
Fig. 5.

Various activities of the weight in different processes, in the second and third phases. The weight matrices are aligned as the same as Fig. 2, V is the weight matrix between the input and the hidden layer, and W is the weight matrix between the hidden and the output layer. The horizontal axis of V represents the ID of input neurons i, and vertical axes of V and W represent the ID of hidden neurons j.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

H j = f ( i l V i , j I i )
O = f ( j m W j H j )
W j n + 1 = W j n + α ( O n T ) O n ( 1 O n ) H j n
V i , j n + 1 = V i , j n + α ( O n T ) O n ( 1 O n ) W j n H j n ( 1 H j n )
τ = L ( M + N ) δ m + [ L ( M 1 ) + N ( L 1 ) ] δ a
τ = ( 2 M + NL + LM + 1 ) δ m + ( LM NL + N L + 3 M ) δ a .

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