Characterizing polarization management in a p-hmpd system

Transcription

1 Characterizing polarization management in a p-hmpd system Rui Zhang and Hong Hua* 3DVIS Laboratory, College of Optical Sciences, University of Arizona, 1630 E. University Blvd., Tucson, Arizona 85721, USA *Corresponding author: hhua@optics.arizona.edu Received 31 October 2007; accepted 26 November 2007; posted 14 December 2007 (Doc. ID 89218); published 23 January 2008 It has been a common challenge to operate optical see-through head-mounted displays in well-lit environments due to the low image brightness and contrast compared with the direct view of a real-world scene. This problem is aggravated in the design of a see-through head-mounted projection display (HMPD) in which the projected light is split twice by a beam splitter and further attenuated greatly by a retroreflective screen. A polarizing head-mounted projection display (p-hmpd) design was recently proposed to enhance the overall flux transfer efficiency and thus increase the brightness and contrast of displayed images. Different from the conventional nonpolarizing HMPD designs, the light polarization states in the p-hmpd system are deliberately manipulated to maximize the flux transfer efficiency, which can potentially result in three times higher efficiency than that of a nonpolarizing HMPD. By measuring the Mueller matrices of the major elements in both a p-hmpd and a nonpolarizing HMPD, we characterize the polarization dependence of each element on incident angles and wavelengths, and also investigate the depolarization effect of the retroreflective screen. Based on these experimental results, we further examine the overall luminance efficiencies of the two types of systems and analyze how various aspects of display performances are affected by the angular and chromatic dependence of the polarization components Optical Society of America OCIS codes: , , , /08/ $15.00/ Optical Society of America 1. Introduction In mixed- and augmented-reality (MR AR) systems [1], optical see-through (OST) head-mounted displays (HMDs) have been one of the basic approaches to combining digital symbols and images with the direct views of real-world scenes through an optical combiner interface such as a beam splitter (BS) [2]. This optical approach allows a user to see the real world in full resolution, which is critical for tasks that require precise eye hand coordination or nonblocked realworld views. Among the various approaches to designing OST- HMDs, the head-mounted projection display (HMPD) method has attracted much interest in recent years because it offers the ability to design wide field-ofview (FOV), low distortion, and ergonomically compact optical see-through displays. This technology was pioneered by Fisher, who first demonstrated the combination of projection optics and a retroreflective screen for a binocular HMD construction [3]. Fergason extended the binocular concept to binocular displays [4] while Kijima and Ojika demonstrated the first head-mounted prototype implemented from offthe-shelf components [5]. Since these pioneering efforts, the HMPD technology has been explored extensively as an alternative to the conventional designs of OST-HMD for various applications, and the technology has evolved significantly [6 18]. Customdesigned optics for HMPDs and a study of retroreflective material properties were initially explored by Poizat and Rolland [6]. Later, Hua and co-workers investigated the engineering challenges in developing a fully custom-designed system and studied the imaging properties of retroreflective materials and their effects on image quality [9,12]. They also designed the first wide FOV, low-distortion, and light- 512 APPLIED OPTICS Vol. 47, No. 4 1 February 2008

2 weight optics for HMPD systems, using advanced optical design technology such as diffractive optical elements, aspheric surfaces, and plastic material [13], which led to the success of custom-designed compact prototypes [11]. Several other efforts were made thereafter to explore more compact or wider FOV display designs using emerging microdisplay technologies such as organic light-emitting diode (OLED) displays and ferroelectronic liquid crystal on silicon (FLCoS) displays [18]. Along with the technology advancements, a wide range of visualization applications, from object-oriented and visual-haptic displays [8,10], medical visualization [7], optical camouflage [14] to multiuser collaborative display environments [15 17], have been demonstrated. Until recently, one of the limiting factors of the HMPD technology was its low image brightness and contrast, which limits the feasibility of applying such information displays outdoors or in well-lit indoor environments such as in operation rooms. A monocular HMPD configuration is schematically shown in Fig. 1. The light from the microdisplay is attenuated due to multiple beam splitting and low retroreflectivity of a retroreflective screen, resulting in a low luminance transfer efficiency of 4%. A polarized HMPD (p-hmpd) design was recently proposed to enhance the overall flux transfer efficiency and thus increase the brightness and contrast of displayed images [19]. Different from conventional nonpolarizing HMPD designs, the light polarization states in a p-hmpd system are deliberately manipulated to maximize the flux transfer efficiency, which can potentially result in three times higher efficiency than that of a nonpolarizing HMPD. In this paper, both nonpolarizing HMPDs and HMPDs are used interchangeably to refer to an HMPD system without the polarization management, although strictly speaking, the performance of HMPD systems based on liquid crystal-type microdisplays shows polarization dependence to some extent. A detailed explanation on the polarization management scheme in the p-hmpd method is to be reviewed in Section 2. Fundamental to the design of a high-performance p-hmpd system, is the quality of polarization management in a wide FOV and broadband system. For instance, the properties of a polarization element can demonstrate considerable variations across a range of incident angles and wavelengths. The angular and chromatic dependence can greatly reduce the overall luminance transfer efficiency and degrade the uniformity of a projected image across the FOV, creating vignettinglike visual artifacts. They can also cause different color shifts in the final image, yielding inconsistent color representations across the FOV. For example, a quarter-wave mica retarder can have as high as half-wave retardance for the 450 nm wavelength light at a 30 incident angle. If the mica retarder is used in a p-hmpd system, it yields almost zero efficiency for the 450 nm wavelength light at a large angle but much higher efficiency for the 550 nm wavelength. The projected image would appear not only severely vignetted from the center FOV to the edge but also in incorrect colors. Furthermore, a retroreflective screen can partially depolarize the incident polarized light. Such depolarization effects usually vary with incident angles as well as wavelengths, which further contributes to the artifacts mentioned above. Therefore, it is highly necessary to characterize the properties of each polarization element and examine how their angular and chromatic variations affect the system performances to guide the future display development. In this paper, we present a set of experiments and procedures to investigate the angular and chromatic characteristics of each polarization component used in a p-hmpd system and the depolarization effects of the retroreflective screen. Based on the experimental results, we further examine the overall luminance efficiencies of a p-hmpd system as a function of FOV and wavelengths, compare against a nonpolarizing HMPD design, and analyze how the various aspects of display performances are affected by the angular and chromatic dependence of polarization components. Fig. 1. (Color online) Schematic of HMPD. 2. Polarization Management in a p-hmpd System The main departure of a p-hmpd from conventional HMPD designs is that polarization states of the display system are deliberately manipulated to maximize the luminance transfer efficiency. A schematic of a monocular p-hmpd configuration is shown in Fig. 2. A polarizing beam splitter (PBS) is used to replace the nonpolarizing beam splitter (BS) in a conventional HMPD shown in Fig. 1. The image on a microdisplay is projected through a projection lens to form a magnified image. To gain the maximum reflection and minimize the transmission loss of the light incident upon the PBS from the projection optics, the light from the image source is manipulated to be s polarized so that its polarization direction is matched with the high-reflection axis of the PBS. After the projected light is reflected by the PBS, it is retroreflected back to the same PBS by a retroreflective screen. Assuming that the retroreflected light 1 February 2008 Vol. 47, No. 4 APPLIED OPTICS 513

3 to account for several factors, including the light emission profile of the pixel, the throughput of the projection system, and the transmittance of the projection system, as these factors vary with microdisplay choices and lens system designs, and should be taken into account during the design process to maximize the flux through the projection system. In the remaining paper, we assume I is constant for both a p-hmpd and a nonpolarizing HMPD, and the luminance transfer efficiency mainly depends on the polarization characteristics of the elements after the projection system in Fig Characterizing Polarization Propagation in p-hmpd Systems Fig. 2. (Color online) Schematic of a p-hmpd system. remains dominantly the same polarization as its incidence light, we place a quarter-wave retarder between the PBS and the retroreflective screen to achieve high transmission through the PBS after the light is retroreflected back. The fast axis of the retarder is set to be at a 45 angle with the polarization direction of the s-polarized light emergent from the PBS. As a result, the projected light is manipulated through a consecutive sequence of polarization states, from its initial state of s polarization to right circular polarization (RCP) after the first pass of the retarder, from RCP to left circular polarization (LCP) at the interface of retroreflective screen, and from LCP to p polarization after the second pass through the retarder. With the above modifications, the projected light is transferred efficiently back to the exit pupil where the eye is positioned for observation. For a pixel on the microdisplay, we denote the viewing angle subtended by the chief ray of the given pixel in the eye space as, which characterizes the FOV of an HMPD system. We use Stokes vector S to describe the polarization properties of the light emitted by the pixel. For a given wavelength, the luminous flux of the pixel collected by the exit pupil of a p-hmpd system can be modeled by I,, S 2 wp,, S r p-trans,, S r C-retro,, S r s-refl,, S I,, S, (1) where l is the luminous flux collected by the projection system from the given pixel and incident upon the PBS, r s-refl and r p-trans are the reflection and transmission efficiencies of the PBS for s and p polarizations, respectively, wp is the transmittance of the wave plate retarder, and r C-retro is the retroreflectance of the retroreflective screen for circularly polarized light. All these parameters above usually vary with the incidence angle, the wavelength, and the polarization state of the light incident upon the associated optical surfaces. For simplicity, in Eq. (1), we use I A. Approach To fully analyze and compare the image quality of p-hmpd and HMPD systems in terms of their overall flux efficiency, image uniformity, contrast, as well as color fidelity, we need to characterize the polarization properties of the elements depicted in Eq. (1) as a function of FOV, wavelength, and incident Stokes vector. For this purpose, we assume a linear interaction of incident light with an element and use a 4 4 Mueller matrix to characterize the polarizationtransformation properties of an element for light at a given wavelength. Each Mueller matrix contains 16 degrees of freedom (DOFs), among which 7 DOFs are associated with nondepolarizing processes: diattenuation, retardance, and polarization-independent loss such as absorption, and the other 9 DOFs are associated with depolarization and describe how different states of polarization are depolarized [20]. With the Mueller matrix description, the incident Stokes vector S Incident for an optical element can be related with the exiting Stokes vector S Exiting by 0 m01 m02 m03 S 1 m 10 m 11 m 12 m 13 S Exiting S S Incident m00 2 m 20 m 21 m 22 m 23 S 3 M S S 1 m 30 m 31 m 32 m 33 S0 S 2 S 3. For each optical element, we measure a series of Mueller matrices at different incident angles with different wavelengths. Based on these matrices, we can obtain the polarization transformations as a function of incident angles, wavelengths, and polarization states. For instance, the reflectance and transmittance of a PBS, the retardance magnitude and the fast-axis direction of a retarder, or the depolarization index and retroreflectance of a retroreflective screen can be derived from the Mueller matrix measurements. Finally, the Mueller matrix of a p-hmpd system at a given FOV and with a given wavelength can be calculated by the multiplication of the Mueller matrices of all the elements following the order of the ray path in Fig. 2. Through the system Mueller matrix, the overall luminance transfer efficiency can be characterized as a function of wavelengths, incident angles, and polarization states. The (2) 514 APPLIED OPTICS Vol. 47, No. 4 1 February 2008

4 resulting image contrast, uniformity, and color fidelity can be further analyzed. B. Experimental Setup An Axometrics polarimeter was used for the Mueller matrix measurements [21]. It consists of a polarization state generator (PSG) that illuminates a testing sample with a series of calibrated polarization states and a polarization state analyzer (PSA) that collects the light transmitted through or reflected from the sample and analyzes the polarization states. Both the PSG and PSA are constructed from a rotating linear retarder and a stationary linear polarizer [21]. While the polarimeter can be calibrated across a broad range of wavelengths, for each sample, we took measurements for three wavelengths, 450, 550, and 650 nm, respectively, to cover the spectral range of interest to displays. Considering that the FOVs of existing HMPDs are typically limited within 60 due to ergonomic factors and the considerably lower retroreflectance at large angles [9], we measured the Mueller matrices of each component from the field angle of 28 to 28 at a 2 increment relative to the on-axis directions. The transmission Mueller matrices of retarders were directly measured with the setup illustrated in Fig. 3(a), in which the PSG and PSA are coaxially aligned and the sample is rotated at a 2 increment from its on-axis orientation. The rotation angle in each setup in Fig. 3 refers to the field angle of the system, and the positive rotation angle is consistent with the positive direction of the system field angle. For the setup in Fig. 3(a), counterclockwise rotation of the sample corresponds to the positive field angles and clockwise for negative angles. For instance, the retarder was initially positioned perpendicularly to the optical axis, and the measurements were taken for incident angles within 28. Similarly the transmission Mueller matrices of BSs or PBS were measured with the setup in Fig. 3(b). The BSs were initially positioned at a 45 angle with the optical axis, and the measurements were taken for incident angles from 17 to 73. In this case, clockwise rotation of the sample is for the positive field angles and counterclockwise for negative angles. The reflective Mueller matrices of BSs and PBS were measured with the setup in Fig. 3(c), in which the PSG is aligned with the optical axis and both the PSA and the samples are rotated from their on-axis orientations for each FOV measurement. The samples were initially positioned at 45 with the optical axis, and the PSA was aligned in a 90 angle with the optical axis. As the samples were rotated, the PSA was adjusted accordingly to analyze the reflected light. Clockwise rotation is for the positive field angles and counterclockwise for negative angles. Fig. 3. Polarimeter setup for polarization measurements of (a) transmittance of a retarder, (b) transmittance of a PBS or a BS, (c) reflectance of a PBS or a BS, and (d) retroreflectance of a retroreflective screen. 1 February 2008 Vol. 47, No. 4 APPLIED OPTICS 515

5 The Mueller matrices of a retroreflective screen cannot be measured directly. They were measured with the setup illustrated in Fig. 3(d), in which the PSG and PSA are aligned in a 90 angle and a nonpolarizing BS was used in the measurement. The reflection and transmission properties of the BS were characterized following the same procedure described above. The PSG, PSA, and BS remain fixed, while the retroreflective screen is rotated from 28 to 28 relative to the on-axis orientation. Counterclockwise rotation corresponds to the positive field angles and clockwise for negative angles. The Mueller matrix of the retroreflective screen at a given field angle and wavelength is then given as M retro, M BS-R 0, 1 M meas, * M BS-T 0, 1, (3) where M retro is the retroreflection Mueller matrix of a retroreflective screen, M BS-R 0 and M BS-T 0 are the reflection and transmission Mueller matrices of the BS at a 45 incident angle, respectively, and M meas is the Mueller matrix directly measured by the polarimeter in Fig. 3(d). 4. Experimental Results A. Polarizing Beam Splitter and Beam Splitters Taking into account the requirements for a wide acceptance angle, a broadband spectral response to the visible wavelengths, and a compact form factor in a p-hmpd display system, we selected a wire-grid (WG) plate PBS custom designed by MOXTEK [22]. The plate thickness is 1.6 mm. Nanometer-scale aluminum WG is deposited on a glass substrate, creating a birefringent structure in which the s polarization sees a mirror and is reflected while the p polarization sees a dielectric film and is transmitted [23]. Based on the transmission Mueller matrices measured at each incidence angle and wavelength, the corresponding transmittance of the PBS for s- and p-polarized incident light are calculated by [24] T s-pbs, 1 2 m 00 m 01 m 10 m 11, (4) T p-pbs, 1 2 m 00 m 01 m 10 m 11, (5) where T s-pbs and T p-pbs are the transmittance of the PBS for the s- and p-polarized light, respectively. Similarly, the reflectance of the PBS for the s- and p-polarized light are calculated by their corresponding reflective Mueller matrices as [24] R s-pbs, 1 2 m 00 m 01 m 10 m 11, (6) R p-pbs, 1 2 m 00 m 01 m 10 m 11, (7) Fig. 4. (Color online) Characterizing the PBS: (a) reflectance of s-polarized light and (b) transmittance of p-polarized light. where R s-pbs and R p-pbs are the reflectance of the PBS for the s- and p-polarized light, respectively. The reflection and transmission performances of a WG-PBS are highly dependent on the wire direction relative to the polarization axis, and also depend on whether the WG film is facing to the incident light. The WG-PBS demonstrates the best performance when the wire direction is parallel to the s-polarization direction of the incident light, and the wire coating is facing toward the incident light. In designing our p-hmpd system, the polarization axis of the light from the microdisplays was manipulated to match with the high reflection axis of the PBS. Figures 4(a) and 4(b) plot the reflectance of the s-polarized light and the transmittance of the p-polarized light, respectively, as a function of the display FOV for the three testing wavelengths. The 0 field angle corresponds to a 45 incidence angle on the PBS. The negative field angle indicates that a ray is incident on the PBS at an angle less than 45. The reflectance for s-polarized light is approximately 90% on average for the 0 field angle, varying between 82% and 96% for field angles in the range of 28. The transmittance for p-polarized light is approximately 87% for the 0 field angle, vary- 516 APPLIED OPTICS Vol. 47, No. 4 1 February 2008

6 Fig. 5. (Color online) Characterizing a BS: (a) and (b) reflectance and transmittance of s-polarized light, and (c) and (d) reflectance and transmittance of p-polarized light. ing between 87% and 60% for field angles in the range of 28. The reflectance and transmittance of the WG-PBS are fairly constant among the three wavelengths and demonstrate low dependence on field angles. In similar manners, we further characterized the polarization properties of a nonpolarizing BS, which was used not only for retroreflective screen characterization, but also for comparing the display performances between a p-hmpd and a conventional nonpolarizing HMPD. Based on the measurements of transmission and reflection Mueller matrices, the transmittance and reflectance of the nonpolarizing BS for s- or p-polarized incident light can be calculated through Eqs. (4) (7) for each field angle and wavelength. The transmittance and the reflectance for nonpolarizing incident light are equal to the m 00 elements of the corresponding Mueller matrices. Figures 5(a) and 5(b) plot the reflectance and transmittance of s-polarized light, respectively, while Figs. 5(c) and 5(d) plot the reflectance and transmittance of p-polarized light respectively. The reflectance for s-polarized light is approximately 55% on average for the 0 field angle, varying between 10% and 85% for field angles in the range of 28. The transmittance for s-polarized light is approximately 45% on average for the 0 field angle, varying between 10% and 87% for field angles in the range of 28. The reflectance for p-polarized light is approximately 25% on average for the 0 field angle, varying between 5% and 46% for field angles in the range of 28. The transmittance for p-polarized light is approximately 45% for 0 field angle, varying between 50% and 95% for field angles in the range of 28. From the graph, the nonpolarizing BS also shows the polarization preference. Compared with the PBS, the reflectance and transmittance of the nonpolarizing BS demonstrated considerably large variations among the three wavelengths and much higher dependence on field angles. B. Retarders A polymer quarter-wave retarder custom made by Bolder Vision Optik [25] was used in our p-hmpd system due to its large FOV and broadband response to the visible wavelengths. Figures 6(a) 6(c) plot the transmittance, the retardance magnitude, and the fast-axis direction of the retarder as a function of field angles at the three wavelengths. The transmittance of the retarder is approximately constant across the entire FOV with less than 1.5% of variation. The retardance magnitude remains approximately constant up to 16 and increases gradually by 20 nm (approximately 3.7% of the testing wavelength) at 1 February 2008 Vol. 47, No. 4 APPLIED OPTICS 517

7 given wavelength. Figure 7 plots the normalized Mueller matrices at the wavelength of 550 nm as a function of incident angles. All the elements in each of the Mueller matrices are normalized by their first element m 00, except the m 00 itself [26]. In this 4 4 graph array, each graph contains the plot of the normalized element value as a function of incident angles only for the wavelength of 550 nm as the measurements demonstrated little dependence on wavelength. The m 00 plot represents the retroreflectance of the screen for nonpolarized light. As expected, it drops with the increase of incident angles. The normalized elements m 11, m 22, and m 33 have the largest absolute values which are on average 0.8, and the m 22 and m 33 have negative signs. The remaining elements of the Mueller matrix plots are generally small, which suggests that the retrorefletive screen has relatively low diattenuation and retardance effects. The depolarization magnitude of a retroreflective screen is quantified by the depolarization index [27]: m 2 2 ij m 00 i,j 1 2 DEP 1. (8) 3m 00 The DEP equals 1 for an ideal depolarizer and equals zero for nondepolarizing Mueller matrices. Figure 8 plots the DEP of a retroreflective screen as a function of incident angles. The DEP is less than 10% for incidence angles within 20, and is less than 23% for angles up to 28. As a result, the retroreflected light remains dominantly the same type of polarization as its incident light, although the retroreflectance would be lower at large incident angles. 5. Analysis of Overall System Performances Fig. 6. (Color online) Characterizing a retarder: (a) transmittance, (b) retardance, and (c) fast-axis direction. A. Luminous Transfer Efficiency The Mueller matrix of the overall p-hmpd system at a given FOV and wavelength is calculated through the multiplication of the corresponding Mueller matrices of each component. Following the optical path in the p-hmpd layout in Fig. 2, it is written as 28. The direction of the fast axis also remains fairly constant at a 45 angle with the optical axis for field angles less than 16, and the angle decreases to 42 at 28 FOV. The transmittance and retardance properties of the retarder demonstrate fairly low dependence on the wavelengths. The variations of the retardance magnitude and fast-axis direction with the incident angle will result in a lower overall efficiency at a marginal visual field of the display than the center, creating vignettinglike artifacts. C. Retroreflective Screen The retroreflective screen used in our p-hmpd system is made of microcorner cubes. The retroreflection Mueller matrices of a retroreflective screen is obtained from Eq. (3) at an incidence angle and a M phmpd, M PBS-T, M retarder, M mirror M retro, M retarder, M PBS-R,, (9) where M PBS-T and M PBS-R are the transmission and reflection Mueller matrices of the PBS, respectively, and M retarder is the Mueller matrix of the quarter-wave retarder. In this equation, we assume the incident light from the projection system has a constant polarization state independent of FOV and wavelength for simplicity due to many engineering factors mentioned in Section 2. For the Mueller matrix calculus, the right-handed coordinate will transform into the left-handed coordinate after retroreflection. As a result, the S 2 and S 3 components in the Stokes vectors will change sign. Since all the single elements were measured under the right-handed coordinate system, 518 APPLIED OPTICS Vol. 47, No. 4 1 February 2008

8 Fig. 7. (Color online) Normalized Mueller matrix plot for the retroreflection of a retroreflective screen at the wavelength of 550 nm. The incident angle is from 28 to 28. a mirror reflection Mueller matrix M mirror is introduced in the formula to maintain the right-handed coordinate system, given as M mirror 1 (10) To make a performance comparison, we further calculate the Mueller matrices of a nonpolarizing HMPD system, in which we assume it shares the same front-end projection system and microdisplays for equivalence. The system replaces the PBS with a regular BS characterized in Subsection 4.A and eliminates the quarter-wave retarder. As a result, the system Mueller matrix is written as M HMPD, M BS-T, M mirror M retro, M BS-R,. (11) Based on the Mueller matrices of the two systems, the overall luminance output through the system can be calculated by Fig. 8. (Color online) Depolarization index versus incident angles., 1, 0, 0, 0 M system, S Incident, (12) where M system is the system Mueller matrix, which equals M p-hmpd for a p-hmpd and M HMPD for a nonpolarizing system, respectively. represents the luminance efficiency of the system when the input Stokes vector has a unit luminance. S Incident represents the Stokes vector of the light from the projection system and it equals 1, 1, 0, 0 for s-polarized light with a unit luminance and 1, 1, 0, 0 for p-polarized light. With the assumption of an s-polarized incident light, Figs. 9(a) 9(c) plot the luminance efficiency of the p-hmpd and nonpolarizing HMPD systems as a function of field angles at three different wavelengths. Figure 9(d) plots the ratio of the luminance efficiency of a p-hmpd to that of a nonpolarizing HMPD as a function of field angles and wavelengths. It indicates that on average the overall efficiency of the p-hmpd is approximately two and half times of 1 February 2008 Vol. 47, No. 4 APPLIED OPTICS 519

9 Fig. 9. (Color online) Luminance efficiency of a p-hmpd and a nonpolarizing HMPD at the wavelength of: (a) 450 nm, (b) 550 nm, and (c) 650 nm. (d) Shows the ratio of the luminance efficiency of a p-hmpd to a HMPD. the efficiency of a nonpolarizing HMPD throughout the entire FOV. The luminance efficiency of a nonpolarizing HMPD was further computed for a p-polarized input. The results clearly show that an s-polarized input yields higher luminance efficiency than a p-polarized input in a nonpolarizing HMPD system. The luminance efficiency of a p-hmpd is on average more than three times higher than that of a nonpolarizing HMPD with a p-polarized input, which agrees well with the efficiency measurements directly obtained from two experimental prototypes in which p-polarized light was utilized in the nonpolarizing HMPD setup [28]. B. Uniformity As shown in Fig. 9, the luminance efficiencies of both p-hmpd and nonpolarizing HMPD systems decrease with the increase of FOV, owning to the angular dependence of the optical transformations for the key optical elements. The reducing efficiencies at large field angles directly result in lower luminance at the edge of the projected image than that of the image center. To quantify the image nonuniformity of the two systems, we calculated the average and the standard deviations (SDs) of the luminance efficiencies as well as the normalized SD value across the FOV for three wavelengths. The normalized SD value, which is calculated through dividing the SD value by the corresponding average, is utilized to characterize the nonuniformity of the luminance efficiency across the FOV and to measure the image nonuniformity. The results are listed in Table 1. The normalized SD value of the p-hmpd system is lower than that of the nonpolarizing system at the wave- Table 1. Uniformity and Image Contrast: HMPD versus p-hmpd HMPD p-hmpd Wavelength 450 nm 550 nm 650 nm 450 nm 550 nm 650 nm Average SD SD Average Contrast APPLIED OPTICS Vol. 47, No. 4 1 February 2008

10 Table 2. Colorimetric Characteristics: HMPD versus p-hmpd FOV (Deg) Red Primary (0.64, 0.33) Green Primary (0.3, 0.6) Blue Primary (0.15, 0.06) White (0.3127, ) HMPD 28 (0.55, 0.39) (0.28, 0.62) (0.17, 0.07) (0.2628, ) 14 (0.60, 0.36) (0.29, 0.62) (0.16, 0.07) (0.2848, ) 0 (0.64, 0.33) (0.30, 0.60) (0.15, 0.06) (0.3113, ) 14 (0.64, 0.33) (0.30, 0.60) (0.15, 0.06) (0.3157, ) 28 (0.61, 0.35) (0.29, 0.62) (0.16, 0.07) (0.2941, ) p-hmpd 28 (0.64, 0.34) (0.30, 0.62) (0.15, 0.07) (0.3177, ) 14 (0.63, 0.34) (0.30, 0.62) (0.15, 0.07) (0.3159, ) 0 (0.63, 0.34) (0.30, 0.62) (0.15, 0.07) (0.3127, ) 14 (0.63, 0.34) (0.30, 0.62) (0.15, 0.07) (0.3105, ) 28 (0.63, 0.34) (0.30, 0.62) (0.15, 0.08) (0.3175, ) length of 450 nm but is higher at the wavelength of 550 and 650 nm. It suggests that p-hmpd has higher image uniformity at the wavelength of 450 nm but lower image uniformity at the wavelength of 550 and 650 nm. C. Contrast The contrast of the projected image for both p-hmpd and HMPD systems is affected by the contrast of the microdisplay itself and the system transformation efficiency. To compare how the contrast of both systems is affected by their luminous transfer efficiency, we assume the microdisplay contrast is 100:1. We further assume that the output light of the display at the white state is dominantly s polarized, and the output at the dark state is unpolarized. Consequently, the Stokes vector for the white state with a unit luminance is 1, 1, 0, 0, and the Stokes vector for the dark state is 0.01, 0, 0, 0, respectively. The output luminance values for both the dark and white states were then calculated using Eq. (12) for both p-hmpd and nonpolarizing HMPD systems. The contrast values of the systems were then obtained by the ratio of the output luminance at the white and dark states. The average contrast values across the entire FOV at three different wavelengths are listed in Table 1. It indicates that a p-hmpd system has higher image contrast than a nonpolarizing system. D. Colorimetric Characteristics The color gamut of a display system, including nonpolarizing HMPD and p-hmpd systems, is determined by both spectral properties of the microdisplay and the luminance transformation through the optical system. As shown in Table 1 and the results in Fig. 9, the overall efficiencies of both systems demonstrate considerable dependence on wavelengths, which could lead to chromaticity shift and reduced fidelity in color representation. To demonstrate how the colorimetric characteristics of the two display designs are affected by different light propagation methods, we assume that the chromaticity coordinates of the red, green, and blue primaries as well as the white point for the microdisplays are the same as those of the standard Red green blue (srgb) display system [29]. Five fields, corresponding to 0, 14, and 28, are used to represent the full FOV. Using the overall luminance efficiencies at the three different wavelengths at these five field angles, we calculated the chromaticity coordinates of the three primary colors and white point after propagating them through both display systems and the results are listed in Table 2. It indicates that the p-hmpd system not only causes less chromaticity shift than a nonpolarizing HMPD system but also better chromaticity uniformity since the chromaticity shifts demonstrate almost no dependence on the field angles in the p-hmpd system. 6. Conclusion and Future Work In this paper, the polarization transformations for both a p-hmpd and a nonpolarizing HMPD were characterized, and the overall optical performance of two display systems was compared from the aspects of luminance efficiency, image uniformity, image contrast, and color fidelity. The results indicate that the p-hmpd system has much higher luminance efficiency and higher image contrast than the nonpolarizing HMPD system. The p-hmpd has higher image uniformity at the wavelength of 450 nm but lower image uniformity at the wavelength of 550 and 650 nm. Both systems show some level of color shifts on the three primary colors and white point due to the chromatic dependence of the luminous transfer efficiency. In comparison, the p-hmpd system not only causes less chromaticity shift but also better chromaticity uniformity than the nonpolarizing system. Among all the optical components, the retroreflective screen is the major factor causing the overall performance degradation in the p-hmpd system. As shown in Fig. 7, the retroreflection of a retroreflective screen is only 23% at the 0 incident angle and drops to 17% at the 28 field angle. The depolarization of the retroreflective screen also contributes to the efficiency reduction. The retroreflective material currently used in our systems is not optimized for imaging optics, but for the traffic control and safety application. In the future, the imaging properties of retroreflective screens will be explored, and the design of retroreflective screen will be optimized for imaging optics in order to further improve the light efficiency and image quality of the p-hmpd system. 1 February 2008 Vol. 47, No. 4 APPLIED OPTICS 521

11 The paper is based on work supported by National Science Foundation (NSF) grants IIS and References 1. R. Azuma, A survey of augmented reality, Presence: Teleoperators and Virtual Environments 6, (1997). 2. J. P. Rolland and H. Hua, Head-mounted display systems, in Encyclopedia of Optical Engineering, R. B. Johnson and R. G. Driggers, eds. (Dekker, 2005), pp R. Fisher, Head-mounted projection display system featuring beam splitter and method of making same, U.S. patent 5,572,229 (5 November 1996). 4. J. Fergason, Optical system for head mounted display using a retro-reflector and method of displaying an image, U.S. patent 5,621,572 (15 April 1997). 5. R. Kijima and T. Ojika, Transition between virtual environment and workstation environment with projective headmounted display, in Proceedings of IEEE Virtual Reality 1997 (IEEE, 1997), pp D. Poizat and J. P. Rolland, Use of retro-reflective sheets in optical system design, Tech. Rep. TR (University of Central Florida, 1998). 7. J. Parsons and J. P. Rolland, A non-intrusive display technique for providing real-time data within a surgeons critical area of interest, in Proceedings of Medicine Meets Virtual Reality 1998 (IOS Ohmsha, 1998), pp N. Kawakami, M. Inami, D. Sekiguchi, Y. Yangagida, T. Maeda, and S. Tachi, Object-oriented displays: a new type of display systems from immersive display to object-oriented displays, in Proceedings of IEEE International Conference on Systems, Man, and Cybernetics (IEEE, 1999), pp H. Hua, A. Girardot, C. Gao, and J. P. Rolland, Engineering of head-mounted projective displays, Appl. Opt. 39, (2000). 10. M. Inami, N. Kawakami, D. Sekiguchi, Y. Yanagida, T. Maeda, and S. Tachi, Visual-haptic display using head-mounted projector, in Proceedings of IEEE Virtual Reality 2000 (IEEE, 2000), pp H. Hua, C. Gao, F. Biocca, and J. P. Rolland, An ultra-light and compact design and implementation of head-mounted projective displays, in Proceedings of IEEE Virtual Reality 2001 (IEEE, 2001), pp H. Hua, C. Gao, and J. P. Rolland, Study of the imaging properties of retro-reflective materials used in head-mounted projective displays, Proc. SPIE 4711, (2002). 13. H. Hua, Y. Ha, and J. P. Rolland, Design of an ultra-light and compact projection lens, Appl. Opt. 42, 1 12 (2003). 14. M. Inami, N. Kawakami, and S. Tachi, Optical camouflage using retro-reflective projection technology, in Proceedings of International Symposium on Mixed and Augmented Reality 2003 (ISMAR, 2003), pp H. Hua, L. Brown, and C. Gao, A new collaborative infrastructure: SCAPE, in Proceedings of IEEE Virtual Reality 2003 (IEEE, 2003), pp H. Hua, L. Brown, and C. Gao, SCAPE: supporting stereoscopic collaboration in augmented and projective environments, IEEE Comput. Graphics Appl. 24, (2004). 17. J. P. Rolland, F. Biocca, F. Hamza-Lup, Y. Ha, and R. Martins, Development of head-mounted projection displays for distributed, collaborative, augmented reality applications, Presence: Teleoperators and Virtual Environments 14, (2005). 18. R. Zhang and H. Hua, Design of a polarized head-mounted projection display using FLCOS microdisplays, Proc. SPIE 6489, 64890B (2007). 19. H. Hua and C. Gao, A polarized head-mounted projective display, in Proceedings of the Fourth IEEE and ACM International Symposium on Mixed and Augmented Reality 2005 (IEEE, 2005), pp R. Chipman, Depolarization index and the average degree of polarization, Appl. Opt. 44, (2005). 21. Axometrics, Inc., MOXTEK, Inc., D. P. Hansen, R. T. Perkins, and E. Gardner, Broadband wire grid polarizing beamsplitter for use in the visible wavelength region, U.S. patent 6,243,199 (5 June 2001). 24. J. Pezzaniti and R. Chipman, Angular dependence of polarizing beam-splitter cubes, Appl. Opt. 33, (1994). 25. Bolder Vision Optik, B. DeBoo, J. Sasian, and R. Chipman, Depolarization of diffusely reflecting man-made objects, Appl. Opt. 44, (2005). 27. J. J. Gil and E. Bernabeu, Depolarization and polarization indices of an optical system, Opt. Acta 33, (1986). 28. H. Hua and C. Gao, Design of a bright polarized headmounted projection display, Appl. Opt. 46, (2007). 29. M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, A standard default color space for the Internet srgb, (1996). 522 APPLIED OPTICS Vol. 47, No. 4 1 February 2008