Dr. Rama Nand Singh Profile

Dr. Rama Nand Singh

Research Staff Member

SPIE Involvement:

Author | Instructor

Proceedings Article | 30 August 2005 Paper

Topics in polarization ray tracing for image projectors

Alan Rosenbluth, Gregg Gallatin, Kafai Lai, Nakgeuon Seong, Rama Singh

Proceedings Volume 5875, 587503 (2005) https://doi.org/10.1117/12.618128

KEYWORDS: Polarization, Ray tracing, Coating, Birefringence, Thin films, Light valves, Prisms, Projection systems, Lenses, Reflection

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Many subtle effects arise when tracing polarization along rays that converge or diverge to form an image. This paper concentrates on a few examples that are notable for the challenges they pose in properly analyzing vector imaging problems. A striking example is the Federov-Imbert shift, in which coating phase-shifts cause a reflected beam to actually be deviated "sideways" out of the plane of incidence. A second example involving groups of coated surfaces is the correction of contrast loss from skew-angle depolarization in the optics of data projectors that use reflective polarization-modulating light valves. We show that phase-controlled coatings can collectively correct the contrast loss by exploiting a symmetry that arises when the coatings are operated in double-pass (due to use of reflective light valves). In lowest order, this symmetry causes any ellipticity that the coatings may introduce in the polarization of illuminating skew-rays to cancel in the return pass from the light valve back through the optics. Even beyond this first order reversibility result, we have shown elsewhere that, for NA less than about 0.2, the computation involved in calculating beam contrast can be reduced to the equivalent of tracing a single ray. We show here that the Federov-Imbert shift can be derived in a straightforward way using this formalism. Even a non-polarizing system will show vector effects when the numerical aperture is sufficiently high, as in photolithographic lenses. Wavefront quality in these deep-UV lenses is of order λ/100, and simulations to account for the complexities of the image transfer steps during IC manufacture must be accurate to better than a part in 1E2 or 1E3; hence small polarization distortions in the superposed image rays become very significant. An interesting source of such distortions is spatial dispersion in CaF₂ lens elements, which gives rise to intrinsic birefringence at the ppm level. Polarization ray tracing must then contend with the phenomenon of double refraction, wherein a given ray splits into two rays each time it passes through an element, giving rise in principle to an exponentially extended family of rays in the exit pupil. However, we show that it is possible to merge each coherent family of rays into a single plane-wave component of the image. (This is joint work with colleagues at Carl Zeiss SMT.¹) Generalizing beyond the analysis of birefringence, such a plane-wave component can be identified with the particular subset of rays that are converged through a common pupil point and transferred to the image after diffracting from the object points within an isoplanatic patch. Thin-film amplitude transfer coefficients implicitly take into account the prismatic change in beam-width that occurs when such a ray bundle refracts through a lens surface, but these coefficients do not include the focusing effect arising from power in the surfaces; hence polarization ray-tracing by sequential application of thin-film transfer coefficients does not by itself provide the correct amplitude distribution over the pupil.

Proceedings Article | 3 May 2004 Paper

Image fidelity verification: contourIFV

Ioana Graur, Rama Singh, Donald Samuels

Proceedings Volume 5379, (2004) https://doi.org/10.1117/12.537490

KEYWORDS: Optical proximity correction, Resolution enhancement technologies, Semiconducting wafers, Photomasks, Image processing, Edge roughness, Optical lithography, Model-based design, Lithography, Image enhancement

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Proceedings Article | 26 June 2003 Paper

Failure prediction across process window for robust OPC

Shumay Shang, Yuri Granik, Nicolas Cobb, Wilhelm Maurer, Yuping Cui, Lars Liebmann, James Oberschmidt, Rama Singh, Ben Vampatella

Proceedings Volume 5040, (2003) https://doi.org/10.1117/12.485478

KEYWORDS: Optical proximity correction, Data modeling, Printing, Image processing, Visualization, Calibration, Binary data, Solids, Failure analysis, Process modeling

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SPIE Journal Paper | 1 April 2002

Optimum mask and source patterns to print a given shape

Alan Rosenbluth, Scott Bukofsky, Carlos Fonseca, Michael Hibbs, Kafai Lai, Antoinette Molless, Rama Singh, Alfred Wong

JM3, Vol. 1, Issue 01, (April 2002) https://doi.org/10.1117/12.10.1117/1.1448500

KEYWORDS: Photomasks, Optimization (mathematics), Reticles, Diffraction, Wavefronts, Algorithm development, Phase shifts, Tolerancing, Resolution enhancement technologies, Detection and tracking algorithms

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Proceedings Article | 14 September 2001 Paper

Optimum mask and source patterns to print a given shape

Alan Rosenbluth, Scott Bukofsky, Michael Hibbs, Kafai Lai, Antoinette Molless, Rama Singh, Alfred Wong

Proceedings Volume 4346, (2001) https://doi.org/10.1117/12.435748

KEYWORDS: Photomasks, Optimization (mathematics), Reticles, Wavefronts, Algorithm development, Diffraction, Tolerancing, Resolution enhancement technologies, Detection and tracking algorithms, Phase shifts

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Proceedings Article | 25 April 2000 Paper

Correction of contrast in projection systems by means of phase-controlled prism coatings and band-shifted twist compensators

Alan Rosenbluth, Minhua Lu, Kei Yang, Kenneth Ho, Rama Singh, Teruhiro Nakasogi

Proceedings Volume 3954, (2000) https://doi.org/10.1117/12.383385

KEYWORDS: Light valves, Polarization, Prisms, Optical coatings, Phase shifts, Wave plates, Projection systems, Reflectivity, Reflection, Mirrors

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Proceedings Article | 20 May 1999 Paper

Projection optics for reflective light valves

Alan Rosenbluth, Rama Singh

Proceedings Volume 3634, (1999) https://doi.org/10.1117/12.349348

KEYWORDS: Light valves, Lamps, Projection systems, Polarization, Reflectors, Reflectivity, Receivers, Prisms, Coating, Glasses

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Showing 5 of 7 publications

Course Instructor

SC889: Layout-Aware Circuit Analysis

This course is directed towards presenting a methodology to include layout effects on circuit analysis. DFM imposes embellishments on the layout to ensure manufacturability with acceptable yields. Traditional circuit analysis and effects of process variability are performed at the schematics level using models for process corners and may lead to excessive guardbanding. Circuit Analysis that is able to predict impact and sensitivity of layout modifications uses circuit simulators together with information derived from litho simulations and helps the designer to ascertain that the layout accompanying the design meets the manufacturability criteria.

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