Near-eye display performance is usually summarized with a few simple metrics such as field of view, resolution, brightness, size, and weight, which are derived from the display industry. In practice, near-eye displays often suffer from image artifacts not captured in traditional display metrics. This work defines several immersive near-eye display metrics such as gaze resolution, pupil swim, image contrast, and stray light. We will discuss these metrics and their trade-offs through review of a few families of viewing optics. Fresnel lenses are used in most commercial virtual reality near-eye displays in part due to their light weight, low volume and acceptable pupil swim performance. However, Fresnel lenses can suffer from significant stray light artifacts. We will share our measurements of several lenses and demonstrate ways to improve performance. Smooth refractive lens systems offer the option for lower stray-light viewing but usually at the cost of a much larger size and weight in order to get to the same pupil swim performance. This can be addressed by using a curved image plane but requires new display technology. Polarization-based pancake optics is promising and can provide excellent image resolution and pupil swim performance within an attractive form-factor. This approach, however, generally results in low light efficiency and poor image contrast due to severe ghosting. We will discuss some of the main limitations of that technology.
Paraxial optics is generally regarded as yielding ideal spherical wavefronts. The ideal point spread function for a circular aperture with an ideal spherical wavefront is an Airy disk. In paraxial optics a small rotation of the exiting polarization state occurs off-axis in the direction perpendicular to the meridional plane. This is a linear form of skew aberration. The resulting apodization of the co and crossed-polarized components in the exit pupil modify the point spread function (PSF) of paraxial optics. In the cross-polarized term, the pupil amplitude varies linearly through a value of zero along the meridional plane, like the function f(x,y) = k x. The Fourier transform of this pupil function is the Fourier transform of the derivative of the Airy disk, which results in a cross-polarized PSF component much larger than the Airy disk. The cause of this polarization rotation, known as skew aberration, is related to the parallel transport of the polarization state through the optical system along skew rays, and to the Berry phase. These cross-polarized PSF components, which although very small in paraxial optics, are nevertheless not zero. Since they occur within paraxial optics they are thus intrinsically interesting. These polarization effects are not related to the Fresnel equations or to any coating–induced polarization but occur in a nonpolarizing or polarizing optical systems.
The point spread function (PSF) for astronomical telescopes and instruments depends not only on geometric aberrations and scalar wave diffraction, but also on the apodization and wavefront errors introduced by coatings on reflecting and transmitting surfaces within the optical system. The functional form of these aberrations, called polarization aberrations, result from the angles of incidence and the variations of the coatings as a function of angle. These coatings induce small modifications to the PSF, which consists of four separate components, two nearly Airy-disk PSF components, and two faint components, we call ghost PSF components, with a spatial extent about twice the size of the diffraction limited image. As the specifications of optical systems constantly improve, these small effects become increasingly important. It is shown how the magnitude of these ghost PSF components, at ~10-5 in the example telescope, can interfere with exoplanet detection with coronagraphs.
An optical design program, Polaris-M, developed at the University of Arizona incorporates many advanced polarization analysis features. At the core of the program is a three-dimensional polarization ray tracing structure used to characterize polarization effects occurring at interfaces and upon propagation through isotropic and anisotropic materials. Reflection and refraction at uniaxial, biaxial, and optically active interfaces are handled rigorously, as well as anisotropic grating structures. By analyzing multiple polarized wavefront components individually, one can study the complicated effects of multiple anisotropic optical elements at the image. Wavefronts can be expanded into polarization aberration terms. Polarized diffraction image formation and polarization dependent optical transfer functions are included.
Diffractive retarders fabricated from gratings in isotropic materials are analyzed by rigorous coupled wave analysis. Calculations show it is difficult to obtain substantial retardance with isotropic phase gratings. Even for an aspect ratio of two, diffractive retarders have a small retardance, < λ/12. Thus it is generally impractical to fabricate quarter wave retarders, much less half wave retarders in plastic or molded glass for example. The dispersion of these gratings is compared to the conventional materials used in the majority of retarders and is found to be very similar. Thus these gratings add little in terms of helping to achromatize retarders
The skew aberration is a form of polarization aberration causes a rotation of polarization states across the pupil. Skew aberration is intrinsic to the optical system depending on the ray path only and whose magnitude is independent of the coatings or other polarization effects. Skew aberration has a much greater effects in high numerical aperture optical systems. A critical angle corner cube system is analyzed as an example to review the skew aberration’s effects.
A new technique is introduced to replace DOEs that are used for illumination in lithographic
projectors with polarization computer generated holograms (PCGHs) that produce both arbitrary
intensity and arbitrary polarization state in the illumination pupil. The additional capability of
arbitrary polarization state adds an additional degree of freedom for source-mask optimization.
The PCGHs are similar in design and construction to DOEs, but they incorporate polarizationsensitive
elements. Three experiments are described that demonstrate different configurations of
PCGHs deigned to produce a tangentially polarized ring. Measurements of ratio of polarization
and polarization orientation indicate that all three configurations performed well. Experimetns
are performed with visible (λ = 632.8nm) light.
Algorithms for polarization ray tracing biaxial materials and calculating the directions of ray propagation and
energy flow, the refractive indices, and the coupling coefficients for all four resultant reflected and transmitted
rays are presented. Examples of polarization state maps, retardance maps and diattenuation maps are generated
as a function of angle of incidence for comparing plane parallel plate systems with uniaxial and biaxial
It is shown that once the diffusely scattered polarization properties are calibrated, the texture orientation can
be calculated directly from diattenuation and retardance. Polarization scattering properties are studied for a
rough aluminum surface with one-dimensional rough texture and well-defined orientation. Functions of Mueller
matrix elements related to sample orientation about the normal via the arctangent function are investigated.
The Mueller matrix bidirectional reflectance distribution function is measured for a linearly sanded aluminum
sample. Sinusoidal fits to the Mueller matrix show that the angular orientation of the data can be recovered
explicitly from its properties.
A custom imaging Mueller matrix retinal polarimeter (the GDx-MM) is built. Mueller matrix images of normal human
fovea were acquired with the GDx-MM over a 9° field at 780nm and have been analyzed for depolarization index and
the variation of degree of polarization with incident polarization state. The degree of polarization (DoP) was often above
50% and varied in complex ways as a function of the incident polarization states. The depolarization properties around
the macula loosely correlated with the retardance image. High spatial frequency depolarizing structures were evident
throughout the fovea.
Depolarization data is provided for several normal retinas. Mueller matrix images of normal human fovea were acquired
with a custom imaging Mueller matrix retinal polarimeter (the GDx-MM) over a 9° field at 780nm and have been
analyzed for depolarization index and the variation of degree of polarization with incident polarization state. The degree
of polarization (DoP) was often above 50% and varied in complex ways as a function of the incident polarization states.
The depolarization properties around the macula loosely correlated with the retardance image. High spatial frequency
depolarizing structures were evident throughout the fovea.
Understanding the interaction of polarized light with materials is critical to applications such as remote
sensing, laser radar, and quality control. The availability of angular and spatial information add additional dimensions
to this understanding.
A facility is constructed for Mueller Matrix Bidirectional Reflectance Distribution (MMBRDF) imaging.
Polarized light at near infrared and visible wavelengths is scattered from samples ranging from bare metals to complex
organic structures with various textures and orientations. The resulting scattered polarized light is measured with a
Mueller matrix active imaging polarimeter.
The in-plane MMBRDF is measured for a sanded aluminum sample as a demonstration of the facility. The
aluminum is found to be a weak depolarizer, with a somewhat higher depolarization index at specular angles.
Retardance is dominated by its linear component and is close to 180° for the majority of angles. Diattenuation is weak,
especially in the specular region, and increases in the region further away from specular angles.
The in-plane Mueller matrix bidirectional reflectance distribution function (MMBRDF) is measured for a Spectralon
calibration target with a reflectance of 99%. Measurements are acquired using a Mueller matrix active imaging,
goniometric polarimeter operated in the near infrared at 1550nm. The Spectralon is measured for both incident and
scattering angles from -80 degrees to 80 degrees to within 20 degrees of retro-reflection. A range of polarization states
is generated and scattered polarization states are analyzed by means of a dual rotating retarder Mueller matrix
polarimeter. Complete Mueller matrix data is measured with a high-resolution camera in image form.
Polarization scatter data is presented in Mueller matrix angular arrays. As expected the Spectralon is a strong
depolarizer and weak s-plane oriented diattenuator. It was also a weak retarder. Diattenuation and retardance are
strongest at horizontal and vertical polarizations, and weakest for circular polarization states.