Planar-integrated Talbot array illuminators

Markus Testorf; Jürgen Jahns

doi:10.1364/AO.37.005399

Planar-integrated Talbot array illuminators

Markus Testorf and Jürgen Jahns

Applied Optics
Vol. 37,
Issue 23,
pp. 5399-5407
(1998)
•https://doi.org/10.1364/AO.37.005399

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Markus Testorf and Jürgen Jahns, "Planar-integrated Talbot array illuminators," Appl. Opt. 37, 5399-5407 (1998)

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Related Topics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction and gratings (050.0050)
- Binary optics (050.1380)
- Fourier optics and signal processing (070.0070)
- Talbot and self-imaging effects (070.6760)
- Micro-optics (350.3950)

About this Article
History
- Original Manuscript: February 23, 1998
- Revised Manuscript: May 8, 1998
- Published: August 10, 1998

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Abstract

We demonstrate the planar integration of Talbot array illuminators designed to generate one-dimensional spot arrays. The array illuminator basically consists of a phase grating and a cylindrical diffractive lens integrated as a single diffractive optical element onto a transparent glass substrate. We discuss various design aspects, and we focus on problems typical for planar-integrated free-space optics like the tilted optical axis of the system. Experimental results and measurements, which were obtained from planar-integrated setups fabricated as surface-relief structures on a transparent glass substrate by use of standard photolithography, are included.

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	Phase of the Transmission Function	Lens Aperture (mm)	Deflection Angle
System 1	$ϕ (x) = - \frac{π}{λ} [{(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α} - 2 {xz}_{D} tan α)}^{1 / 2} + {(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α} + 2 {xz}_{D} tan α)}^{1 / 2}]$	1	α = 13.6°
System 2	$ϕ (x) = - \frac{π}{λ} [{(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α_{o}} - 2 {xz}_{D} tan α_{o})}^{1 / 2} + {(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α_{o}} + 2 {xz}_{D} tan α_{o})}^{1 / 2}] - \frac{2 π}{λ} (sin α_{o} - sin α_{i})$	0.5	α_i = 12.5°α_i = 24.3°
System 3	$ϕ (x) = - \frac{2 π}{λ} [{(x^{2} + z_{D}^{2})}^{1 / 2} + x sin α]$	0.75	α = 10°
System 4	$ϕ (x) = - \frac{π}{λ z_{D}} {(\frac{2}{{cos}^{3} α} + 1)}^{- 1} x^{2}$	2	α = 16.5°

	Working Distance z = M/N z _T	Number of Features per Period	Phase Values (π/2)	Spot Size (δ/d)	Efficiency of Infinite Grating
System 1	N = 15, M = 5	8	0- 1- 3- 0- 3- 3- 1	1/8	96%
System 2	N = 3 , M = 1	3	1- 0- 0	1/3	94%
System 3	N = 10, M = 3	5	0- 0- 2- 3- 2	1/5	92%
System 4	N = 16, M = 15	8	0- 0- 1- 2- 0- 2- 1- 0	1/8	96%

	Diffraction-Limited Line Diameter δ_f (μm)	Measured Line Diameter δ_f (μm)	Efficiency of Infinite Grating	Measured Efficiency per Period (Central Part)
System 1	5.7	10	96%	89%
System 2	13.8	16	94%	92%
System 3	7.0	12	92%	85%
System 4	11.8	17	96%	90%

	Phase of the Transmission Function	Lens Aperture (mm)	Deflection Angle
System 1	$ϕ (x) = - \frac{π}{λ} [{(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α} - 2 {xz}_{D} tan α)}^{1 / 2} + {(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α} + 2 {xz}_{D} tan α)}^{1 / 2}]$	1	α = 13.6°
System 2	$ϕ (x) = - \frac{π}{λ} [{(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α_{o}} - 2 {xz}_{D} tan α_{o})}^{1 / 2} + {(x^{2} + \frac{z_{D}^{2}}{{cos}^{2} α_{o}} + 2 {xz}_{D} tan α_{o})}^{1 / 2}] - \frac{2 π}{λ} (sin α_{o} - sin α_{i})$	0.5	α_i = 12.5°α_i = 24.3°
System 3	$ϕ (x) = - \frac{2 π}{λ} [{(x^{2} + z_{D}^{2})}^{1 / 2} + x sin α]$	0.75	α = 10°
System 4	$ϕ (x) = - \frac{π}{λ z_{D}} {(\frac{2}{{cos}^{3} α} + 1)}^{- 1} x^{2}$	2	α = 16.5°

	Working Distance z = M/N z _T	Number of Features per Period	Phase Values (π/2)	Spot Size (δ/d)	Efficiency of Infinite Grating
System 1	N = 15, M = 5	8	0- 1- 3- 0- 3- 3- 1	1/8	96%
System 2	N = 3 , M = 1	3	1- 0- 0	1/3	94%
System 3	N = 10, M = 3	5	0- 0- 2- 3- 2	1/5	92%
System 4	N = 16, M = 15	8	0- 0- 1- 2- 0- 2- 1- 0	1/8	96%

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