## Abstract

The system design of front-projection systems for free-form screens utilizing conventional single-aperture optical layouts always requires a trade-off between system complexity and achievable luminous output. This article presents novel slide pre-processing algorithms based on array projection technology that are able to resolve the design drawbacks for both free-form as well as strongly-inclined planar screen applications by breaking the common contradiction between system simplicity and flux. Starting from describing common design strategies and their drawbacks, the theoretical basics of the novel concept are investigated and applied to raytracing simulations. Experimental results are shown and evaluated regarding their optical performance.

© 2013 Optical Society of America

## 1. Introduction

The projection of sharp images onto strongly inclined or free-form screens while maintaining a simple optical layout with sufficient flux is a challenging problem of current projectors.

Current approaches for solving this issue can be divided into two main design strategies: While the first concept utilizes free-form optical elements to ensure focusing on free-form screens, the second one is based on an inherent large depth of focus (DoF) of the optics that matches or exceeds the required screen geometry. While the first concept increases the complexity of the optical system but keeps the projected flux, the second concept maintains the complexity of the optical system but reduces the luminous output. Thus, applications with demanding specifications regarding flux mostly utilize complex free-from optics to ensure a certain image quality and brightness [1].

We propose a novel slide pre-processing algorithm based on array projection technology [2] that is able to break these constraints of conventional projector design while maintaining simple, planar and flexible optics. While past and recent publications solely focus on technical advantages of array projectors that arise from the inherent decoupling of étendue and system volume, this article presents a novel optical feature that is based on the large depth of focus of the individual projectorlets [2, 3]. Starting with a short comparison of current optical concepts for free-form screen projection, we describe the basic working principle before examining mathematical algorithms utilizing paraxial system descriptions. After a verification done by raytracing simulations, the article is concluded by experimental results of first prototypes verifying the potential of the proposed concept.

## 2. Single aperture projector concepts for free-form screens

The multitude of existing projector design concepts adapted for free-form screens can roughly be decomposed into two main strategies, depicted in Fig. 1.

- a) The first concept utilizes either free-form slides and/or free-form optics in a single-aperture setup to create sharp images onto free-form screen surfaces [Fig. 1(a)]. Thus, a large system étendue and luminous output can be maintained for a given source luminance. However, accordant systems tend to be bulky and contain complex optics with non-rotational symmetric elements with demanding sophisticated manufacturability and high initial cost. This approach requires customized optical surfaces for each individual screen geometry, resulting in costly and inflexible system designs.
- b) The second concept is based on a large inherent depth of focus of a single-aperture projector that matches the requirements defined by the screen geometry [Fig. 1(b)]. This inevitably leads to a decreased aperture size which reduces the available system étendue and flux for a given source luminance. However, this approach results in simple and compact systems that are more flexible regarding varying screen geometries.

## 3. Array projection fundamentals

This section describes the fundamentals of array projection, which is the key technology for the algorithms presented in this article.

An array projector, working for a perpendicular planar screen, consists of a two-dimensional arrangement of microprojectors (projectorlets) superimposing their identical subimages to an integral image on the screen [2]. Herein, only single image distances were considered, that solely require a pitch difference of identical subslides w.r.t. the projection lenses. While the small focal lengths of the microlenses in the range of some millimeters ensure dramatic slimness improvement w.r.t. single aperture projectors, a sufficient brightness of the composite image is generated by integrating the flux contributed by each projectorlet. A basic array projector layout is shown in Fig. 2.

The manufacturing of according microlens arrays is based on a well-established polymer-on-glass technology with reflow mastering. Experimental results of a sample prototype are depicted in Fig. 3. The microoptics realized in the framework of this article utilize the same array layout, lens shape design and manufacturing methods described in [2].

## 4. Application of array projection to free form screens

In addition to prior work, which focused on compactness and flux as main technical benefits of array projection technology, this article utilizes the large depth of focus of each single microprojector, derived in [2,3], and applies it to tilted and free-from screens. Therefore we drop the identity of all subslides and derive a unique mathematical correlation of an arbitrarily shaped 3D image and its corresponding 2D object array. The application of the resulting algorithm is promising to overcome the technical drawbacks of current design strategies [Fig. 1] by utilizing the inherent large étendue and low complexity of an array projection setup along with its unique depth of focus properties.

The basic setup of an array projector for free-form screens is depicted in Fig. 4. Analogue to [2] it consists of an array of projectorlets, each containing a lenslet imaging its corresponding subslide to a composite real image onto the 3D screen surface having an axial distance L to the array plane. The projectorlets are characterized by their common focal width f and individual decentration Δx w.r.t. the array center. The 3D screen is treated as a set of planar screens with infinitesimal lateral extension perpendicular to the optical axis represented by their lateral position x’ and their axial distance to the array plane L_{n}. Due to hyperfocally working projectorlets [3, 4] we neglect image blurring caused by marginal rays and we restrict our considerations on chief-raytracing.

The mathematical composition of 3D image information and 2D slide array information is obtained by paraxial backward raytracing [5] starting from the screen side of the setup. Each image point x’ corresponds to a set of slide points x depending on the decentration of their corresponding projectorlet Δx according to

_{n}, x´, the microlens array parameters represented by f, Δx and the resulting 2D subslides represented by x. The composition of all pre-corrected subimages generates a sharp integral image onto an arbitrarily shaped 3D surface while maintaining a large overall pupil size and luminous flux.

## 5. Simulation

We simulate the performance of an accordant array projector for a strongly-inclined screen to clearly demonstrate the principle of operation. Therefore we transfer an accordant array projector setup to a real raytracing software (Radiant ZEMAX) and analyze its performance.

We choose both, an uncorrected and corrected array projector for direct contrast transfer comparison of line grid projection [Fig. 5]. The results of the contrast measurements demonstrate drastical improvement of image quality in comparison to conventional projectors. Other than the standard Scheimpflug geometry for tilted screen projection [6], the proposed system does not require tilted object planes.

## 6. Prototype realization

Based on results of raytracing simulations, an optical design was calculated considering LED étendue and luminous flux, system slimness and image quality. The single projectorlet has a focal width of 2mm and an f-number of 2.5. The array contains 149 hexagonally packed projectorlets with a pitch of 797µm, resulting in a lateral footprint of the microlens array (MLA) of 11x11mm^{2}. Each projectorlet consists of a polymer plano-convex condenser lens and a projection lens on the opposite side of a common glass substrate. The proposed slide pre-processing algorithm according to Eq. (3) was successfully implemented into a novel CAD based design tool. Therefore we wrote a Ruby -programming language based- plugin for Trimble Sketchup Pro 2013^{®}. The obtained object information is written into a chromium layer buried below the condenser lens array.

We chose two different test setups. The first one utilizes a 70° tilted planar screen with an axial distance of 400mm referring to the center of the MLA. A set of significant test images was selected to characterize the optical performance experimentally. According to Eq. (3), these test images are converted into a 2D array of slides. Figure 6(a) shows exemplary results of mask data generation for this screen setup. As expected, the slide geometry corresponding to a marginal projectorlet shows a significant deformation w.r.t the slide of the center projectorlet [Fig. 6(b)]. These well-defined slide variations are crucial for perfect overlap of the individual subimages and integral image quality. The second test setup contains a triple of non-overlapping perpendicular subscreens in three different distances. The image on each subscreen corresponds to its individual distance (20cm, 40cm, 60cm).

The manufacturing processes of the microoptical components [Fig. 7] are based on polymer-on-glass replication of reflow microlenses - a well-established wafer-level technology - already successfully applied in mass production [7, 8].

## 7. Results

We successfully realized accordant microoptical elements on 4” wafers. We characterized equivalent array projector chips with and w/o pre-corrected slides to ensure fair performance benchmarking and system evaluation. Therefore, we classified two test setups: tilted and facetted screens.

#### a) Tilted planar screen

The visual comparison of projected images [Fig. 8] shows significant improvement of image contrast conservation for both near and far screen distances. A more detailed analysis of projected line patterns, as depicted in Fig. 9, confirms these observations by numerical contrast measurements. The area of sufficient image quality could be enhanced by a factor of four.

#### b) Facetted perpendicular screen

The chosen test setup consists of a facetted 3D screen containing three perpendicular subscreens in 200mm, 400mm and 600mm distance to the projector MLA [Fig. 10(a)]. The experimental results [Fig. 10(b)] clearly approve that the algorithms presented in this article are capable to realize projections onto any 3D surface solely by utilizing a manipulated 2D slide array.

## 8. Conclusion

Based on array projection technology we present a novel approach for projecting images on inclined or free-form screen surfaces while conserving system simplicity and flux. The generation of a superposed screen image created by a multitude of projectorlets, each having a large depth of focus, allows for simple screen geometry pre-correction solely by 2D slide manipulation according to the proposed mathematical algorithm. The basic principle and its mathematical background as well as a novel CAD based design tool for slide mask generation are successfully approved by experimental results of first prototypes showing significantly improved image quality. Summing up, the proposed algorithm is able to combine technical advantages of microoptical array projectors - compactness and brightness –along with new design flexibility regarding screen geometry [2]. We believe that this concept will open up new lighting and projection applications with severe requirements regarding system volume, flux, robustness, and flexibility.

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