Abstract

A compact and modular optical system that employs gradient-refractive-index rod lenses to image arrays of Lambertian sources is characterized both experimentally and by ray-tracing simulations. A hybrid optical system that incorporates additional microlens arrays to reduce transmittance losses and aberrations is also modeled, and the two systems are compared.

© 1997 Optical Society of America

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Figures (17)

Fig. 1
Fig. 1

Differential pair of optical thyristors.

Fig. 2
Fig. 2

Optical plane-to-plane imaging system. BS, beam splitter; I/O, input–output.

Fig. 3
Fig. 3

Photograph of the optical system.

Fig. 4
Fig. 4

Ray-intercept error (a) Δy and (b) Δx as a function of the incident-ray slope for three object positions.

Fig. 5
Fig. 5

Field curvature.

Fig. 6
Fig. 6

Geometrical spot diagram: Fields 1–3 are at (x, y) = (0, 0), (0.8, 0.8), and (1.25, 1.25) (millimeters), respectively.

Fig. 7
Fig. 7

Results of radiometric analysis for a source on axis (center) and at (1.25, 1.25) (millimeters) (corner).

Fig. 8
Fig. 8

Experimental and theoretically calculated transmittance plotted as a function of the radial distance of the source from the axis.

Fig. 9
Fig. 9

8 × 8 array of optical thyristor differential pairs imaged through the optical system. The center separation of each pair is 95 µm × 100 µm.

Fig. 10
Fig. 10

Intensity profile in the image plane (projected on the x axis) of a single thyristor source at various positions on the x axis of the object plane.

Fig. 11
Fig. 11

rms spot widths obtained from intensity profiles compared with results obtained from radiometric analysis.

Fig. 12
Fig. 12

Power received in the detector window as a fraction of the power contained in the image spots and fractional cross talk into neighboring pair elements plotted as a function of object position.

Fig. 13
Fig. 13

Test grid imaged through the system to measure distortion. The grid pitch is 100 µm × 100 µm.

Fig. 14
Fig. 14

Variation of the maximum blur-spot diameter as a function of the index-gradient parameter n 20 of the second lens.

Fig. 15
Fig. 15

Diagram of the use of a microlens array to reduce the effective divergence angle of the light emitted by the thyristors.

Fig. 16
Fig. 16

Approximate determination of the optimum microlens diameter d.

Fig. 17
Fig. 17

Comparison of hybrid and GRIN-only systems transmittance.

Tables (2)

Tables Icon

Table 1 rms Spot Widths and Blur-Spot Diameters Calculated for the System

Tables Icon

Table 2 Comparison of GRIN-Lens and Hybrid GRIN-Microlens System Performance

Equations (7)

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nr=n00+n10r2+n20r4,
nr=n001-A2r2,
A=-2n10n00.
l=1n00AtanAZ,
NA=n00r01-Ar022A1-R21-R2 sinϕ1/2,
feff=1n00A sin ZA,
dxf# sin θmax,

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