Download Imaging and Non-imaging System Modeling in ASAP

ASAP TECHNICAL PUBLICATION
BROPN1155 (JANUARY 11, 2008)
Imaging and Non-imaging System Modeling in ASAP
The purpose of this technical publication is to describe how ASAP®, the Advanced Systems Analysis
Program from Breault Research Organization, Inc. (BRO), supports the tools necessary to simulate both
imaging and illumination systems. The comprehensive imaging and illumination simulation capabilities in
ASAP are demonstrated by modeling a liquid crystal display (LCD) projector.
Figure 1. Projector system made of ideal (paraxial) lenses
BRO technical publications referenced in this document may be viewed or downloaded from the BRO
Knowledge Base, http://www.breault.com/k-base.php.
Breault Research Organization, Inc.
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Imaging and Illumination System Modeling
All optical systems contain both imaging and non-imaging or illumination systems. This is illustrated in
overhead, slide, and liquid crystal display (LCD) projectors. The illumination system provides light to the
slide or LCD, which is then imaged to a screen by the projection or imaging system. Even an automobile
headlight can be considered an illumination system with your eyes providing the imaging function.
Since all optical systems contain both imaging and non-imaging systems, any optical engineering software
should be able to simulate both system types. This is necessary for complete end-to-end, seamless
simulation, regardless of whether the optical software is a lens design or analysis program.
Turning system requirements into physical properties (software capabilities)
General system performance requirements dictate the optical configuration from concept to first-order to
final design. There are many different and sometimes industry-specific performance requirements for
systems using imaging and illumination systems. The primary optical performance requirements for the LCD
projector include requirements for both the imaging and illumination systems. The requirements are
interrelated and the total system performance is dependent on both systems. In addition to industry
requirements, today’s LCD projectors must conform to mechanical (styling), electrical, manufacturing,
weight, and cost requirements. The principal performance requirements of the LCD projector are total screen
lumens, screen illumination uniformity, color balance, color uniformity, and image quality, which are usually
expressed as resolution (modulation transfer function (MTF) and image size (magnification)). But if we dig
more deeply into the origin and meaning of these requirements, we see that we can relate them to
fundamental radiometric and photometric properties.
Radiometry literally means the measurement and geometric characterization of power. We geometrically
characterize power in terms of projected areas and solid angles. Power per unit solid angle is called intensity.
Power per unit projected area is called irradiance. And power per unit projected area per unit solid angle is
called radiance. Intensity and irradiance can be obtained by appropriate integration of the radiance.
Photometry is really a normalized form of radiometry. Normalization is a process where a measurement or
calculation is made to conform to a standard or established norm. The established norm in the case of
photometry is the response of the human eye.
Given these definitions, it is not difficult to see that our LCD performance requirements are related to the
photopic normalization of power and its subsequent geometric characterization in terms of projected areas
and solid angles. Total screen lumens, color balance, and uniformity are related to luminous power, screen
illumination uniformity is related to illuminance, and resolution is related to irradiance of a point source.
ASAP can compute these radiometric quantities as well as their photometric counterparts including color
coordinates. Refer to the technical guide, Radiometric Analysis, for more information regarding radiometry,
photometry, and colorimetry in general.
In the context of ASAP, radiometry means the calculation of these quantities. Common threads bind the
calculation of the radiometric quantities together. These commonalties are found in fundamental parameters
that completely specify the behavior of electromagnetic (EM) radiation. This information is needed to
compute radiometric, photometric, and colorimetric properties. These characteristics are coherence,
polarization, amplitude, and phase. Light and its interaction with optical elements are physically and
mathematically distinguished and defined primarily by these characteristics. Given these four characteristics
and the optical system behavior, we can compute the system’s power, intensity, irradiance (exitance),
radiance, and color properties. ASAP can simulate and calculate all of them.
The relationships between the optical performance requirements are based upon knowledge of optics,
experience, patents, other external inputs such as benchmarking, and inherently, the simulation software. The
physical properties derived from the optical performance requirements are used as input into the software
programs. The important point is that these inputs dictate the type of software tool needed for the problem
2 Imaging and Non-imaging System Modeling
and not the reverse. The software tool must have the capabilities to accurately simulate the physical
properties that affect performance.
Table 1 summarizes the optical performance requirements introduced above for simulating the imaging and
illumination systems of an LCD projector, the first-order optical design parameters they drive, and the
software capabilities required to simulate the related physical properties. The table is not a comprehensive
listing of the relationship between all system requirements and physical properties (software capabilities). It
is a guide to understanding the relationship between some requirements and which software capabilities and
features are needed to simulate the illumination and imaging systems of an LCD projector system. The
optical properties from one category can affect the performance in other categories.
Table 1. Relationship between performance requirements, optical properties, and physical properties
Optical Performance
Requirements
First-Order Optical Properties
Physical Properties/Software
Capability (Feature)
Throughput (Total Screen
Lumens)
-source
-source near-field structure
-collection optics (etendue 1)
-light valve (LCD)
-imaging lens
-optical coatings
-source power
-near- and far-field emission properties
-optical and mechanical data (lens
curvatures, thickness, refractive indices,
etc.)
-light valve transmission
-coating prescription
Screen Illumination Uniformity
-source
-illumination optics
-light valve
-cosine fall-off
-opto-mechanical data
-source radiance maps
-light valve spatial/angular uniformity
Color Balance/Uniformity
(CIE Color Coordinates)
-source
-dichroic filters
-light valve
-color channel optics train
-source power spectrum
-coating prescriptions
-light valve spectral transmission
-opto-mechanical data
Image Quantity and Quality
(Point Spread Function,
Modulation Transfer Function,
Resolution,
Visualization)
-magnifications
-image sizes
-image positions
-source coherence
-polarization (Fresnel calculation)
-amplitude (Fresnel calculation)
-phase (optical path length, aberrations)
-bitmap simulation
Coherence, polarization, amplitude, and phase affect total screen lumens, illumination uniformity, color
balance and uniformity. ASAP allows you to create sophisticated source models according to these physical
properties. ASAP then automatically changes the polarization, amplitude, and phase of light as it interacts
with optical components. For example, ASAP changes the polarization and amplitude of light incident on an
interface according to Fresnel’s equations. It also adjusts the phase of the light according to the indices of
refraction, optical path length, and aberration of the optical components. ASAP automatically uses this
information to compute radiometric and photometric performance.
Measurements also are a crucial input for the design process. Your software program must be able to accept
measured data to perform realistic analyses. Measurements quantify the physical properties of your optical
system. The accuracy of the simulation is directly influenced by the quality of the measured data. Original
equipment manufacturer (OEM) suppliers are sometimes unwilling or unable to supply data you need for the
simulation. So be prepared to measure or have measured the physical property yourself. Measurements are
1
The numeric value of the etendue is a constant of the system. It is calculated as the integral over the product of the
differential area of the opening size of an optical system and the solid angle within which the system accepts light.
Imaging and Non-imaging System Modeling 3
Imaging and Illumination System Modeling
still the best course of action even though many software packages include material databases for simulating
some physical properties. At least check the information from supplied databases used in your simulations
against measured data for accuracy. If you do not, you could end up with a bad design. For example, if you
use incorrect coating information, the radiant and colorimetric output from your simulation will be incorrect.
Or if you are using a source with the wrong emission properties, the screen illuminance will be incorrect.
Optical design analysis process: simulating imaging and illumination systems
The optical design and analysis process involves computing the first-order properties, aberrations and
radiometry (photometry) of the imaging and illumination components individually and as a system. Optical
engineers design both types of systems, but engineers designing illumination systems are commonly called
illumination design engineers, and engineers designing imaging systems are called optical designers. These
designers often use different tools, techniques, and software to achieve their respective designs. For example,
the optical designer relies more on the concept of a point source than an extended source for designing and
evaluating the imaging optical system. The optical designer also uses lens design codes. On the other hand,
the illumination designer relies more on extended sources for designing and evaluating illumination systems.
The illumination designer also uses computer-aided design (CAD) software and optical analysis codes to
design optical systems.
In either case, the mathematical models used by optical engineers in this process are primarily geometrical
optics and physical optics. Geometrical optics simulates light as a series of lines or “rays” propagating
through space. Geometrical ray tracing is a fundamental part of geometrical optics. A ray trace involves
intersecting a line, the ray, with a mathematical surface. This is equivalent to finding the roots that
simultaneously solve both equations. The laws of refraction (Snell’s law) and reflection are subsequently
applied to optically transform the ray. Physical optics simulates light as a wave phenomenon that accounts
for the “spreading” or diffractive behavior of light. The rays of geometrical optics are the normals of the
wavefronts of physical optics from a point source. Extended sources are collections of point sources. Note
that these models do not describe the actual nature of light, but rather its behavior under a prescribed set of
physical conditions.
Source tools of the designer
The source itself is a distinguishing difference between the tools that the optical and illumination engineers
use to design and analyze their optical systems. A point source is a mathematical construct. It is a point
singularity of emission on a source. Physically, the smallest point source is an atomic level emitter. Point
sources emit spherical waves of radiation. The surface of constant phase of the light from the point source is
called a wavefront. Extended sources are made up of many such point sources.
The emission of light from a point source can also be represented by a set of rays. A ray is a purely
geometrical concept, it does not exist physically. It is basically a vector that simulates radiative transfer. The
spatial point of the ray vector is its location in space or in the optical system. The direction of the ray vector
is the propagation direction of the radiation. The power of the ray can be considered the magnitude of the
vector.
4 Imaging and Non-imaging System Modeling
Rays are normal to the wavefront. Wavefronts are surfaces over which the optical path lengths of rays
(refractive index of the material the ray is in, multiplied by the distance the ray travels in the material) from a
point source have the same length. Figure 2 illustrates the wavefront concept.
Figure 2. Point source, rays, and associated wavefront in 2D
Having established the fact that extended sources are made of point sources and point source are described
by a collection of phase related rays, we would assume that extended sources are ensembles of point sources
whose rays are related in phase. However, extended sources used in general illumination design and
specifically in ASAP are really not simulated in this manner. Instead, a Monte-Carlo technique is used where
each point source of the extended source is represented by a single ray. A very large number of such rays
comprise the extended source. This is done for physical and mathematical reasons.
Physically, many different types of extended sources are used in illumination or non-imaging systems where
we are not concerned about the phase relationship between the rays of a single point source or its neighbors
of the extended source. We are typically interested in the incoherent addition of the point source’s flux or
power with other point sources, and their subsequent geometric characterization into intensity, irradiance,
and radiance. The phase information is not needed for this calculation. Mathematically, we need many rays
for statistical accuracy to simulate extended sources, and we save time and computer disk space by tracing a
single ray from a point source, instead of many rays from the point source since we do not need the
wavefront.
However, ASAP allows you to simulate both the point sources normally associated with imaging systems
and the extended sources normally associated with illumination systems. You can even use extended sources
with imaging systems or point sources with illumination systems. ASAP provides a common, seamless
illumination and imaging simulation environment without the need for special illumination and imaging
paths.
For more information on modeling point and extended sources see the technical publication, Modeling
Sources―Incoherent, Extended.
The first-order properties of an optical system are those parameters that refer to its image properties, such as
image location, magnification, and effective focal length. The first-order properties of imaging and
Imaging and Non-imaging System Modeling 5
Imaging and Illumination System Modeling
illumination systems can be separate or different, depending on whether the illumination system is based
upon an imaging concept such as Köhler illumination (see the section, Geometric modeling). The aberrations
of an optical system are those parameters that refer to the image quality produced by the optical system, such
as point spread function (PSF), ray fan plot, and modulation transfer function (MTF). Optical system
aberrations are usually associated with imaging and not illumination systems, because an aberration is the
departure of the ideal behavior of a point source from its actual behavior in an imaging system. The
photometry of an optical system includes those radiometric parameters that refer to the amount of light,
normalized to the response of the human eye, transmitted by the optical system to the image.
The first-order properties, aberrations, and photometry are all related to the parameters of the point and
extended source. For example, the size of the extended source, or alternatively the maximum extent of a
point source on the extended source along with the object, determine the illumination system magnification.
The size of the object, along with the image, determines the imaging system magnification. Magnification is
a first-order property. Optical designers use this information with the mathematical tools of first-order optics,
such as the y-y bar diagram, Gaussian reduction, paraxial imaging, and the power transfer equation, to
translate the first-order properties into a preliminary system layout, which serves as a starting point for the
actual lens design. Some designers also use patent applications and experience to generate design starting
points. Generally, the first-order properties of the illumination system and imaging system are first
determined and then used to layout the optical elements for the actual design.
Defining the optical design process
The optical design process means different things to different people. Designers of classical lens systems,
such as projection (imaging) lenses, primarily use commercially available “optical design” software
packages, which are essentially lens design programs. Lens design codes are geometrical ray trace simulation
programs that utilize some form of an automated mathematical optimization algorithm to determine an
optimum lens design for a given set of conditions. The lens design code automatically changes element radii
of curvature, thickness, spacing and refractive indices, while performing and evaluating geometrical ray
traces, to force the optical system to conform to a certain merit function. You can think of the automated lens
design process as a kind of feedback loop. Lens design codes are efficient at finding solutions to this type of
problem and creating an optical prescription.
Engineers designing illumination systems make much more use of CAD software in the actual optical design,
but they also use optical analysis packages as well. Optical analysis codes are used to analyze those
phenomena that cannot be easily simulated in lens design codes—phenomena such as the extended sources
of illumination systems. Illumination engineers primarily use the CAD program to layout both the
mechanical and optical surfaces of the optical system. This mechanical information is then translated to the
optical analysis program, which is used to simulate the interaction between light from sources and the optical
and mechanical structures. In this process, the optical and mechanical geometries are not entered in a script
form as in lens design codes, but are inherent in the graphical CAD description.
Unfortunately, not only are the specific simulation and optimization features of lens design codes not
available in a CAD system, they usually are impractical to use in illumination systems. For example, it is
difficult or impossible for lens design codes to model some of the unusual illumination system geometries,
extended sources, and non-sequential ray trace behavior. An extremely large number of rays are needed for
the statistical accuracy to simulate the extended sources of illumination systems in a Monte Carlo ray trace.
These ray traces typically take a significant amount of time, even in a very fast ray tracer like ASAP. Large,
Monte Carlo ray traces used with lens design optimization routines, which involve an algorithm trying to
solve a non-linear problem while requiring a minimum of hundreds of iterations to reach a local minimum,
render this process intractable. ASAP includes a set of powerful, general optimization algorithms that, when
combined with a properly defined merit function, can be very effective for illumination optimization.
6 Imaging and Non-imaging System Modeling
Illumination system simulation
Before an image can be seen, it must be illuminated. So the first thing that must happen is the design and
analysis of the illumination system. Rule one for illumination engineering is that there is never enough light.
This is important because an optical system cannot produce a brighter image than that of the source
supplying light to the optical system. This conservation of brightness is the thermodynamic limit of light
concentration. What is really conserved is the etendue (see footnote 1). Many optical engineers refer to the
throughput as the “A-Omega” product because it is the product of the cross-sectional area of a beam at a
location in the optical path and its projected solid angle. The power loss in the optical system is due to
transmission losses.
The consequence of these interactions is that the luminance (lumens/projected area/solid angle) at the LCD is
the luminance of the source with power losses. The luminance of the image of the LCD at the screen is the
luminance of the LCD (or source) with the appropriate power losses. A calculation of the throughput at the
beginning of the design process can help determine whether the illumination component will meet any
system level luminance requirements. Moreover, it is important that the simulation software properly
simulates sources and any optical element coatings that affect power loss. ASAP is able to simulate the near
and far-field properties of sources and the prescription or measured behavior of optical coatings.
Source simulation
A common projection source is the plasma discharge lamp. It is an extended source that is not spectrally
homogeneous. This means that the different wavelengths that a source emits correspond to spatially different
emitting volumes. These types of sources are difficult if not impossible to simulate in most optical design
and analysis programs. However, ASAP has a powerful source simulation capability that allows you to Abel
transform a 2D bitmap radiance picture from such a discharge source to create a 3D emitting volume. This
emitting volume is an excellent model describing the near-field emission properties of the source in terms of
a ray density apodization. See the technical publication, Modeling Sources―Incoherent, Extended, for a
description of ray density and flux weighted apodization.
By default, a correctly color-captured bitmap is converted into three constituent colored bitmaps. Each
bitmap in turn is Abel transformed to create volume sources with primary colors of red, green, and blue. See
Figure 3. For even more spectrally detailed source simulation, you can record and transform any source
wavelengths you chose, creating accurately, spectrally apodized, source power spectral distributions.
Imaging and Non-imaging System Modeling 7
Imaging and Illumination System Modeling
Asymmetric arc
Modified Abel transform
Figure 3. CCD image of an asymmetric arc, its modified Abel transform, the red, green, and blue
components of another arc, together with the full color image
ASAP can also simulate incoherent filament, fluorescent, and LED sources. The ASAP Light Source Library
features many common automotive bulbs and LEDs, and other source models.
Geometric modeling
ASAP is similar to 3D solids modeling programs in that it utilizes a powerful geometrical modeling
approach. This approach permits a nearly limitless variety of systems to be constructed in a CAD file, or
through the command language. For more information on CAD, see the technical publication, CAD in ASAP.
As opposed to other ray tracing algorithms found in lens design codes, all surfaces and ray data in ASAP are
referenced by default to a single global coordinate system. Smooth, continuous object surfaces can be
represented by a sequence of simple conicoids or a general polynomial with up to 286 terms. Therefore,
anything from a simple plane to an arbitrarily oriented elliptical toroid can be modeled precisely. ASAP can
also simulate parametric mesh surfaces (NURBS). In fact, polynomial and parametric entities can be used to
trim each other. Polynomial and parametric surfaces can even be made into emitters in ASAP.
Abel transformed sources in ASAP, or any ASAP source, can be combined with the opto-mechanical
modeling capability in ASAP to construct source geometries. The Abel transformed source is a ray density
apodized source whose properties simulate the near-field emission properties of the source. The near-field
properties of the source are the emission properties close to the source.
Near-field emission properties are a function of both the spatial location and angular propagation direction of
the ray from the source. These source models are combined with the opto-mechanical structure of the source,
which in large part determines the far-field emission properties of the source. The far-field properties are
primarily a function of the angular propagation direction of the ray from the source.
Physically, the far-field emission pattern is obtained when we observe the source from such a large distance
that it appears to be a point having no spatial resolution. Figure 4 illustrates the complicated geometry of a
discharge source.
8 Imaging and Non-imaging System Modeling
Figure 4. Discharge source geometry
Complicated source geometries are only part of what ASAP can simulate. ASAP can accurately model
virtually any optical-mechanical system and its optical properties. Figure 5 shows an ASAP model of a
complicated, yet common type of mosaic lens found in Köhler illumination systems. The most common
types of illumination systems for projectors are critical and Köhler systems. ASAP can model both types and
their many variants.
Figure 5. ASAP model of an LCD projector with a non-sequential mosaic lens
In traditional Köhler illumination the source is actually imaged into the entrance pupil of the projection lens.
The illuminated object is placed close to the condenser, where the light is uniform. The entrance pupil of the
projector lens is simply the image of the aperture stop formed by all the optical elements located before the
aperture stop.
The aperture stop is the physical aperture in the projector lens assembly that limits the amount of light
through the optical system. Therefore, by imaging the source to the entrance pupil of the projector lens,
optical engineers maximize the amount of light getting through the aperture stop. A modified Köhler
illumination system consists of a two-stage condenser. The first condenser forms an image of the source in
Imaging and Non-imaging System Modeling 9
Imaging and Illumination System Modeling
the aperture of the second condenser, which in turn images the first condenser on the object. In effect each
point on the source illuminates the entire object, and each point on the object is illuminated by the source.
In a critical illumination system, the source is imaged to the object. However, critical illumination requires
homogenized sources, which are commonly created with integrating rods, light pipes, and homogenizers.
Such a homogenizer is illustrated in Figure 6.
Figure 6. Discharge source and homogenizer
ASAP also simulates diffuse illumination systems, which can be made with diffusing screens or cavities. If a
diffuser screen is not used, fluorescent tubes are commonly used as sources with a redirecting light pipe. A
diffusing cavity and simple fluorescent tubes are illustrated in Figure 7. Lambertian diffusing screens and
sources, such as white paints and fluorescent tubes, have a uniform brightness with a luminous intensity
(lumens/solid angle) that falls off with the cosine of the angle from the surface normal.
Figure 7. Backlight system using a diffusing cavity and fluorescent tubes
10 Imaging and Non-imaging System Modeling
An interesting point about diffusers is that in a sense they destroy the conservation of etendue. These devices
drastically change the solid angle into which a given amount of power is redirected. Subsequent optical
elements or our eyes see reduced luminance. Consequently, many back-lit systems use peened surfaces in
light pipes. Peened surfaces are small bumps or dimples in the light pipe that cause light to spread without
scattering losses as shown in Figure 8.
Figure 8. Peened surface
Diffuse illumination systems are most commonly found in back-lit display systems such as laptop computers
and consumer electronics. They are photonically challenged and not sufficiently light efficient to be used
with projection display systems. In addition to the scattering surfaces of diffuse illumination systems, ASAP
allows you to create databases of optical properties that describe real and complex refractive indices with
absorption or gain, complex multilayered coatings, uniaxial crystals, and polarizers. Although the LCD is a
birefringent polarizing optical element, it is rarely simulated in ASAP.
The Fresnel equations are used not only to calculate transmission losses at interfaces between two dielectric
media as a function of incident angle and polarization, but also reflection losses at any dielectric/conductor
interfaces. Moreover, ASAP is capable of splitting any ray into transmitted, reflected, diffractive, near
specular, diffuse, and backscatter components. Many of these features are illustrated in the polarization
converter in Figure 9.
Figure 9. Polarization converter
For example, LCDs commonly use crossed linear polarizers as light conditioning components. The extended
sources used in the illumination systems are randomly (naturally) polarized. The linear polarizers transmit
Imaging and Non-imaging System Modeling 11
Imaging and Illumination System Modeling
only approximately 50% of the naturally polarized light. Polarization converters are used to recover some of
this lost light. Polarization converters convert naturally polarized light into a preferential linear state.
Polarization converters are composed of a linear array of polarizing beamsplitters and alternating halfwave
plates. The polarizing beam splitters reflect the S-state of polarization while passing the P-state. The P-states
pass through the halfwave plates where they are converted into S-states. ASAP can simulate the halfwave
plate and even the polarization beamsplitter coating.
Imaging system simulation
Again, illumination systems are only part of the total optical system. When an optical engineer computes the
first-order properties of an imaging system, the engineer is computing quantities such as projector system
magnifications, depths of field and focus, estimated resolutions, the geometrical image location, and size of
the LCD on a screen. The optical engineer lays out the first-order design of the optical system as a thin-lens
model. The basic theories and equations used, such as the imaging equation, are what most college freshmen
learn in the two weeks covered on optics in their physics course on electrodynamics. These are also
parameters that are treated in a strictly geometrical manner. They can be derived from purely geometrical
arguments or from a power series expansion of a ray tracing equation. They are the “first-order” terms of the
power series expansion of a ray tracing equation.
ASAP is ideally suited to help both optical and illumination designers investigate first-order optical system
behavior and conceptual design spaces. The IDEAL lens in ASAP allows you to simulate the ideal or
paraxial behavior of optical elements by knowing only their first-order optical properties, such as effective
focal length. In fact, the entire projection system illustrated on the cover of this technical publication is made
of ideal lenses.
Imaging systems produce images, which are only as good as the aberrations induced by the optical
components of the imaging system and acquired by the resulting image. Computing the aberrations of the
optical system involves computing the image quality of the imaging component of the optical system, usually
by ray tracing point sources.
Aberrations to an optical engineer are departures of the behavior of the optical system performance from
ideal behavior. Ideal behavior is based upon the concept of the point source. Objects to geometrical optical
engineers are really extended sources made up of individual point sources. Light travels as rays from a point,
the point source. Different point sources on the object are referred to as field points or field angles (for
objects at infinity, such as stars). Ideal point-to-point behavior results when all the rays from such a point in
the object space (for example the LCD) propagate or are traced through the optical system and cross at a
single conjugate point in image space (such as the screen) with the same optical path lengths. If this does not
occur, the original point source is not a point in the image plane and the system suffers from aberrations.
The most common types of aberration are spherical, coma, astigmatism, field curvature and distortion. There
are also chromatic aberrations due to the dispersion of the glasses in the projector optics. In other words,
light at different wavelengths does not focus at the same points in space, because optical materials have
different refractive indices for different wavelengths of light.
Fortunately, most optical systems, particularly imaging systems, can be simulated with geometrical ray
tracing. However, geometrical optics does not account for the spreading of light due to diffraction, which is a
wave phenomenon, unless you are using ASAP. When all the aberrations of an optical system are corrected,
the system is said to be "diffraction limited". The minimum spot size obtainable in the imaging component is
determined entirely by diffraction, as is the imaging resolution. The pixels of the LCD have to be imaged to
the viewing screen.
12 Imaging and Non-imaging System Modeling
How do you know if your projector lens can resolve and image the pixels of the LCD on the viewing screen
without significant degradation? A common rule of thumb used by optical engineers to estimate minimum
resolutions is that the minimum, on axis, diffractive spot size that a lens can produce is the "f"-number of the
lens in microns. The "f"-number is the effective focal length of the projection lens divided by its clear
aperture. It is the same definition as the "f"-number in photography and is an indication of the “speed” of the
optical system. For example, an "f"/2 system is considered a “fast” system. It produces a minimum spot size
of approximately 2 microns at the viewing screen.
Performance issues are limited not only to the projector optics. Somebody is looking at the image produced
by your display system. Remember that the eye is the final optical system for all display systems. It also has
a minimum resolution. This value is one arc minute (there are 60 arc minutes in a degree) in most optics
texts, a computed number consistent with experience.
Imaging system source
Just as the illumination system has a source, so too does the imaging system. It is the object illuminated by
the illumination system. Furthermore, the light from the illumination system must propagate through the
projection optics, so the projection optics also affect the quantity and quality of the screen illumination.
Optical engineers designing and analyzing imaging optical systems quite often use point sources. Spot
diagrams, point spread functions, ray fan plots, wave aberration plots, and MTFs are the primary evaluation
tools found in lens design codes, all of whose outputs are based upon a point source input. The MTF is a plot,
at many field positions, of the resolution of an imaging system in terms of a normalized contrast ratio as a
function of spatial object frequency. The performance of your display system changes with field position
(LCD size) or angle because most of the aberrations in your optical system, which partially determine
resolution, also change as a function of field position or angle.
Lens design codes incorporate these tools in merit functions that drive the lens parameters, such as radii and
thickness to optimum values that minimize the merit function. ASAP also has these capabilities, including
optimization and tolerancing features. Rather than providing a series of specialized merit functions that are
effective for a limited range of applications, optimization in ASAP consists of a set of very general
optimization techniques that can be applied to a wide range of imaging and illumination design problems,
using merit functions based on any user-specified design objectives. BRO continues to improve and extend
the optimization and tolerancing capabilities in ASAP.
Point sources and the information they yield about an optical system provide significant numerical
information about the performance of the optical system. It is sometimes difficult to convey the performance
numerical information of the optical system to non-technical managers and decision-makers, especially when
design changes are needed that cause potential cost and schedule impacts. Fortunately, BRO has developed
and incorporated visualization techniques into ASAP that allow for far more realistic, powerful, and flexible
2D and 3D scene visualizations. ASAP can simulate scenes as geometrical rays that can then be traced
through your optical system to the image plane. As the rays propagate through the optical system they
acquire the aberration and power loss imparted to it from the optical system as a function of field angle and
pupil position. In a sense, the rays individually and quantitatively sample the performance of the optical
system, while their contributions as a whole become a qualitative visualization of the image quality of the
systems.
ASAP can convert a 2D bitmap scene into constituent red, green, and blue (RGB) components. Each
component is then converted into a 2D ray set. The rays in each pixel are assigned the same flux (power) and
the power contribution of the pixel to the entire scene is adjusted by controlling the number of rays in the
Imaging and Non-imaging System Modeling 13
Imaging and Illumination System Modeling
pixel. The irradiance of the entire bitmap is used as a probability density function to set the total number of
rays per pixel. This ray density apodization approach, as opposed to a flux-weighted apodization is ideally
suited for the Monte Carlo ray trace simulations. Figure 10 illustrates a scene represented as a set of rays that
will be imaged through an optical system.
Figure 10. Scene represented as a set of rays for re-imaging through an optical system
Each component RGB set of rays is traced through the optical system resulting in a composite image at the
image plane. The RGB image is then converted back into a bitmap, which represents the performance
visualization.
Figure 11 illustrates an original bitmap “object” and its simulated “image”.
Figure 11. Original bitmap (top) and simulated image (bottom)
Ghost images, scattered light, lens tolerances, defects and defocus as well as diffraction can be included in
these calculations as illustrated in Figure 12. ASAP can also simulate 3D scenes.
14 Imaging and Non-imaging System Modeling
Figure 12. Ghost images
Summary
All optical systems contain both imaging and non-imaging or illumination systems. For this reason, any
optical engineering software should be able to simulate both system types. This is necessary for complete,
end-to-end, seamless simulation regardless of whether the optical software is a lens design or analysis
program. ASAP can handle both types of systems individually and together. The optical modeling capability
in ASAP allows the simulation of optical systems from the source to the object to the image in a single
software program.
References
"Non-rational and rational parametric descriptions for the geometric propagation of light in an optical
system," Kevin J. Garcia, Ph.D. Dissertation.
“Geometrical optical modeling considerations for LCD projector display systems”, John Schweyen, Kevin
Garcia, Philip Gleckman, SPIE Vol. 3013.
“Optical engineering for display systems”, Kevin Garcia, Information Display, March 1997.
“Computer simulation of asymmetric arc lamp volume emitters”, Michael Stevenson, Marie Côté, Chris
Campillo, David Jenkins, Proceedings of SPIE: Optical Design and Analysis Software v. 3780-17 (1999).
“Optical system image irradiance simulations”, Marie Côté, John Tesar, SPIE International Optical Design
Conference, June 1998.
“Optical system performance visualization”, Marie Côté, Bob Pagano, Michael Stevenson, Proceedings of
SPIE: Optical Design and Analysis Software v. 3780-01 (1999).
Imaging and Non-imaging System Modeling 15