![Examples of different pixel geometries in flat panel displays, and their sub-pixel placements. (a) RGB vertical stripe display, (b) RGB delta, (c) VPX (with three subpixels/pixels), and (d) VPW (with four subpixels/pixels). [9]](https://www.researchgate.net/publication/339669360/figure/fig2/AS:865172059074560@1583284501061/Examples-of-different-pixel-geometries-in-flat-panel-displays-and-their-sub-pixel_Q320.jpg){kind=tracking}
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Received: 10 November 2019 Revised: 21 January 2020 Accepted: 4 February 2020
DOI: 10.1002/jsid.878
REGULAR CONTRIBUTED PAPER
The effects of source resolution on resolution enhancement
through shifted superimposition projection
Svein Arne Jervell Hansen1,2 Jon Yngve Hardeberg3Muhammad Nadeem Akram1
1University of South-Eastern Norway,
Borre, Norway
2Barco Fredrikstad AS, Gamle
Fredrikstad, Norway
3NTNU, Teknologivegen 22, Gjøvik, 2815,
Norway
Correspondence
Svein Arne Jervell Hansen, University of
South-Eastern Norway, Raveien 215, 3184,
Borre, Norway.
Email: svein.a.hansen@usn.no
Funding information
Norges Forskningsråd, Grant/Award
Number: HiLase 245569
Abstract
Resolution in a projected display is traditionally defined by the number of pix-
els in the projector's spatial light modulator (SLM). In recent years, different
techniques that increase the resolution on the screen above the number of SLM
pixels have gained popularity. In one such technique, called pixel-shifting or
shifted-superimposition, the display physically shifts every nth frame on the pro-
jected screen, and the overlapping pixel grids forms a finer subpixel grid with a
higher pixel count.
There is still an open question how much this method increases the resolution
and how to quantify it. The resolution on the screen also depends upon the
resolution of the input image fed to the projector.
In this work, we experimentally investigate how the projector performs
with resolution enhancement through pixel-shifting and how this method
relates to the source resolution. We also investigate some known methods
of resolution measurement and evaluate how these methods perform for the
shifted-superimposition case.
We find that the resolution enhancement through shifted-superimposition
enhances the resolution to about 40% over native resolution, and we also find
two different measurement methods (grille contrast and least resolvable line
pair method) that is relevant for effectively measuring resolution within such
systems.
KEYWORDS
display measurements, image processing, image quality, projected display, resolution,
superimposition
1INTRODUCTION
Resolution is one of the key performance parameters of a
projector, and the projector industry continuously aims to
increase it. Superimposition of projected images is a cost
effective way of enhancing the resolution in a projector
above the native resolution of the spatial light modula-
tor (SLM). Superimposition may be implemented either
with a multi-projector setup,[1] with an optomechanical
system within a single projector,[2] or as a static optical
setup within a single projector.[3] As long as a superimpo-
sition consists of two or more images superimposed on one
projected surface, the resulting image will be an additive
function of the projected images.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the
original work is properly cited.
© 2020 The Authors. Journal of the Society for Information Display published by Wiley Periodicals, Inc. on behalf of Society for Information Display
J Soc Inf Display. 2020;1–12. wileyonlinelibrary.com/journal/jsid 1
2JERVELL HANSEN ET AL.
Since the market drives for 4K and 8K images and
video, resolution enhancement techniques in displays
have gained some momentum. High resolution SLMs are
seldom cost effective, and not all technologies have mod-
ulators available with such a high pixel count. For these
kind of modulator technologies, it is appealing to push the
resolution above the native resolution of the SLM. Even
though the actual pixel count on the projected screen will
increase, the resolution enhancement method also intro-
duces some artefacts in the image. Because the optical
overlap of superimposed images acts like a low-pass fil-
ter, some high frequency content is lost in the image.[4]
The spatial artefacts manifest as blurring in the image, and
these artefacts impacts both the visual quality and the res-
olution measurements. The introduced artefacts raise the
question of how high resolution is actually achieved, and
which factors do impact this resulting resolution.
In a projected pixel-shifted display, every nth frame is dis-
placed on the wall with subpixel precision. The two most
common shift configurations are either half a pixel in one
diagonal[2] (two positions as in Figure 1), or half a pixel in
both diagonals (four positions).[4] By shifting in the diago-
nals, we are producing a new grid of overlapping subpixels
where all pixels are of equal size and shape.
Pixel-shifted displays challenge the traditional sense of
resolution as this is a computational display and not a
traditional display[5]. Each resulting subpixel is made up
of the sum of the SLM pixels illuminating the resulting
pixel, and each subframe is contributing to this. Because
different subframes may include different details from the
high-resolution source image, there will be more details
present on the screen than the native resolution would be
able to represent without the pixel-shifting technology.
For the different subframes to be able to display dif-
ferent details from the source image, the source image
must be of higher resolution and therefore contain more
details than the native SLM resolution. This means that
the resolution of the source image will affect the amount
of available details for the projector to generate subframe
details and will therefore also affect the perceived res-
olution of the resulting superimposed image. While the
increased perception of quality and resolution in shifted
superimposition have been proved,[6,7] the actual resolu-
tion gain itself have not been established. In this work,
we experimentally investigate the relationship between
source resolution and resulting superimposed resolution,
and also how the resulting superimposed resolution is to
be faithfully measured.
The rest of the paper is organized as follows: section 2
presents different definitions of resolution and approaches
to how one may measure the display resolution. Section 2.1
includes which methods we choose to use in this work and
also how we set up the experiments. The measurements
themselves are presented in section 2.2 and discussed in
section 2.3. Finally, the last section concludes on how the
source resolution affects the resulting resolution and how
the selected measurement methods perform.
2RESOLUTION MEASUREMENT
Display resolution is in its simplest form is defined as the
number of pixels in the display available to form a image.
This definition applies to all traditional forms of displays,
and in a projected display, the resolution would be the
number of pixels in the SLM. There are at least two aspects
of the display that challenge this simple definition of res-
olution: the quality of the pixels and the physical build of
the pixels.
The quality of the pixels may be seen as the pixels ability
to represent different details. In most displays, the pixels
are not completely independent of each other and will in
some form affect the pixels in near proximity with their
own value.
This may for instance be as nonperfect optics in pro-
jected displays, backlight bleeding in LCD monitors, or
as fringe field effects in LCD and liquid crystal on silicon
(LCOS) displays.[8] All of these effects make the value of a
pixel interfere with the appearance of the neighbour pix-
els. Shifted superimposition as a resolution enhancement
method will add dependencies between some neighbour
pixels because of the optical overlap of the pixels and also
because the SLM pixels illuminate a larger area than one
resulting pixel in the superimposed pixel grid.
The physical build and geometry of the pixels may also
affect the perceived resolution of the displayed image. Pro-
jected displays usually have a uniform pixel grid where
the colors are superimposed on each other within the
same pixel grid. But other displays may have different pixel
geometry, for instance flat panels with subpixel rendering
where colors are adjacent to one another and arranged in
a specific pattern. Even though each pixel in Figure 2 [9] is
made up of a red, green and blue sub-pixel, those colored
subpixels may be individually controlled to form differ-
ent pixel pairs to increase the apparent resolution when
needed.
These aspects illustrate the point of having a more thor-
ough resolution definition than just the pixel-count. For a
given display, it will give direct information to measure the
different specifications of the display thereby also the res-
olution. By using the same measurement methods, it will
then also be possible to compare the performance of differ-
ent displays. There is currently no measurement standard
that is agreed upon by all display manufacturers in all
markets, but there have been several measurement stan-
dards proposed. The International Committee for Display
JERVELL HANSEN ET AL.3
FIGURE 1 Subframe 1 and Subframe 2 shifted half a pixel diagonally from each other. The overlap results in a finer subpixel grid
consisting of approximately twice the amount of pixels in both horizontal and vertical direction. The resulting finer pixel grid is illustrated at
the far right with the edges trimmed off. In this illustration, we see that the new finer pixel grids have a pixel size of approximately a quarter
of the original pixel size
FIGURE 2 Examples of different pixel
geometries in flat panel displays, and their
sub-pixel placements. (a) RGB vertical stripe
display, (b) RGB delta, (c) VPX (with three
subpixels/pixels), and (d) VPW (with four
subpixels/pixels).[9]
Metrology (ICDM) have included several proposals for spa-
tial resolution measurement in the Information Display
Measurements Standard (IDMS).[10]
2.1 Least resolvable line pairs
The least resolvable line pairs measurement is an estab-
lished method for determining resolution based on mea-
suring a limited number of line pairs.[11] This is done by
displaying an object in 3D-space consisting of a predeter-
mined number of line pairs. The object is then pushed back
in 3D space further and further away, apparently shrinking
the line pairs. When the line pairs are at the limit where
they are nearly not resolvable anymore, the physical size
of the line pairs is measured. The size of the whole pro-
jected screen is then divided by the size of a single line pair.
By doing these measurements both horizontally and verti-
cally, the total resolvable resolution in the system may be
obtained.
One major drawback with this method is that it is
very prone to subjective biases and measuring errors. The
action of establishing when the line pairs are at their
resolvable limit is in itself very subjective. In addition to
that, any inaccuracy when measuring the physical size of
4JERVELL HANSEN ET AL.
FIGURE 3 Contrast modulation example as shown in the
Information Display Measurements Standard (IDMS) standard.
Measurements are done with Grilles of 1, 2, 3 and 4 pixels width,
while linear interpolation makes up the intermediate values
the line pairs may have a major impact on the total res-
olution number. Another trait of this method is that it is
measuring the system performance of the image genera-
tor, the projected display, and the screen at the same time.
This fact may be a feature for a system integrator, but for
measuring the display itself, it introduces uncertainties.
Another drawback is that the results of this method will
be dependant on the image generator. This could make
this as a characterization method hard to compare objec-
tively over different test sites and technologies. On the
other hand, it is a good system-level resolution measure-
ment method for fixed installations with in-system image
generators. For these reasons, it is a method often applied
in the simulation industry where the display is a fixed
component in the system.
2.2 Grille contrast modulation
The grille contrast modulation method is to measure the
Michelson contrast with grille patterns (alternating black
and white stripes) with different widths. The intermediate
values between these points is extracted from linear inter-
polation between neighbour points as shown in Figure 3.
This approach was proposed by The ICDM within the
Society for Information Displays (SID) in 2012 when they
released the IDMS.[10]
The contrast vs line pair curve gives an indication on
what contrast the display is able to reproduce for differ-
ent detail sizes. In this sense, the curve gives not only a
resolution measurement, but also a quality factor to that
given resolution. It is debatable what contrast factor that
is really needed for different display applications. IDMS
proposes that the display itself should have 50% contrast
modulation for text applications and 25% contrast modula-
FIGURE 4 Spatial Frequency response example curve from
Information Display Measurements Standard (IDMS). MDis the
frequency modulation for the display
tion for image applications. This means that the resolvable
resolution at 25% contrast modulation is
ResolvableResolution =Displa𝑦edResolution∕nr(1)
In the example given in Figure 3, the calculated grill line
width nris 1.16, making the resolvable resolution lower
than the input resolution to the display with a factor of
1.16.
2.3 Slanted edge measurement
The slanted edge method is to measure the spatial fre-
quency response (SFR) as an approximation of the modu-
lation transfer function (MTF). This method has become
widely used within fields of optics, and has been adopted
by multiple international standards within optics, includ-
ing International Organization for Standardization (ISO)
and Institute of Electrical and Electronics Engineers
(IEEE). The slanted edge approach for displays is described
in the IDMS chapter 7.7.[10]
In this method, we measure the luminance of vertical or
horizontal step patterns on the display with a slightly tilted
camera so that the sampled image captured by the CCD
camera oversamples the slanted edge. The SFR is then cal-
culated as described in chapter 7.7 of the IDMS to obtain
the MD(𝑓)curve. An example of such a curve is shown in
Figure 4.
The SFR obtained by the slanted edge method give a
continuous spectrum without the linear approximation
as introduced by the Grille Contrast Modulation method.
This means that the resolvable resolution numbers at 25
and 50% contrast modulation are calculated more precisely
than those methods that use linear approximation between
measured points.
For both the slanted edge method and the grille contrast
method, there is an ongoing debate regarding the appropri-
ate contrast modulation required for different applications.
In the IDMS, 25 and 50% for images and text respec-
JERVELL HANSEN ET AL.5
tively is suggested as points of interest in the slanted edge
method also.
3EXPERIMENTAL SETUP
In our experimental setup, we used a Barco F70-4 K
pixel-shifted projector equipped with a Barco EN41 lens.
This projector has a native Wide Quad Extended Graphics
Array (WQXGA) (2560 by 1600 pixels) digital micromirror
device (DMD) as an SLM and a pixel-shifting mode where
every other frame is shifted half a pixel diagonally. To cap-
ture the test scenes, we used a Nikon D5100 SLM camera
with a 23.6×15.6 mm 16.2 megapixel complementary
metal-oxide-semiconductor (CMOS) sensor. The captured
images was stored in Nikon's uncompressed raw format
Nikon Electronic Format (NEF). The setup is shown in
Figure 5.
One purpose of these tests is to explore the relationship
between the source resolution and the resulting measured
resolution. To this end, all of these experiments are per-
formed for different source resolutions, starting at the
native WQXGA resolution. Then the experiment is redone
several times with steps of 10% increase in the source res-
olution all the way up to 120% over the native resolution.
3.1 Line pair measurements
To perform the least resolvable line pair measurements, we
used a regular PC as the source connected to the projector.
On this PC, we had a program rendering a 3D object con-
sisting of three black/white line pairs. This object could be
moved back in 3D space to increase the distance between
the viewpoint and the object thus also decreasing the
size of the object on the screen. This will be viewed as
the line pairs is shrinking all the way down to not being
distinguishable anymore. The measurement setup was as
illustrated in Figure 6A where there is an observer who
determines if the line pairs are resolvable or not.
The experiment itself was performed as described in
section 2.1. The object with the line pairs was moved away
from the viewpoint until the three line pairs was not resolv-
able anymore. Then the object was moved towards the
viewpoint one step again to make them resolvable. At this
point, the physical size of the line pairs on the screen was
measured. The total size of the projected surface was then
divided upon the line pair size to calculate the number
of line pairs that would fit within the projected area. This
number is the measured resolution for this method at this
given source resolution. The measurements in this paper
is done by a single observer, who is a professional from the
display industry.
The least resolvable line pair measurement is redone for
source resolutions ranging from native SLM resolution up
to 220% of the native SLM resolution.
3.2 Grille contrast measurements
The grille contrast measurement experiment setup was per
section 2.2. On the PC, we had a program rendering three
black/white line pairs of controllable width, and we did
the measurements with 1-, 2- , 3-, and 4-pixel-wide lines.
Measurements were done using the camera and dcraw
was used to convert raw image files to Description Tagged
Image File Format (TIFF) format. The images were then
filtered and analysed in MATLAB as described in IDMS
chapter 7.2.
The measurement setup was as illustrated in Figure 6B
where the camera is capturing the test scene.
3.3 Slanted edge measurements
The slanted edge measurement experiment was setup as
per section 2.3. On the PC, we had a program rendering
a black/white step pattern. The measurements was done
with the camera that we tilted 5 degrees relative to the edge
of the step pattern. The raw image files were converted
to TIFF images with dcraw before they were filtered and
analysed in Matlab as described in IDMS chapter 7.7.
The measurement setup is the same as for the Grille con-
trast modulation method as illustrated in Figure 6B, but
with a different test image displayed and with the camera
tilted 5 as described in chapter 7.7 of the IDMS .
There are several commercial software solutions avail-
able for calculating the slanted edge response of an image,
but we did not find any that suited this use case. The nature
of the DMD makes the projected pixels very distinctive
with dark gaps in between, and the available software solu-
tions required a solid line edge to calculate the response.
For this reason, we developed our own solution that took
the distance between the pixels into account, and sampled
one line for each pixel in the area of interest. Even though
the shifted superimposition reduces the screen-door effect
significantly, Figures 11 and 14 illustrates that the resulting
subpixels also are distinguishable. So for calculating the
slanted edge of the shifted superimposed scenes, we took
the resulting pixelsize into account, which in this case is
half the size of the projected DMD pixel of the native image
in Figure 14A.
4RESULTS
4.1 Least resolvable line pairs
The least resolvable line pair measurement was executed
as described in chapter 2.1. In these measurements, the
source resolution is set to WQXGA, the native resolution of
the projector, and then increased in steps of 10 up to 120%
over the native resolution.
6JERVELL HANSEN ET AL.
FIGURE 5 Lab setup measuring the
projected contrast with a camera
FIGURE 6 A, Test setup for
the least resolvable line pair
method. B, Test setup for the
grille contrast and the slanted
edge methods
Figure 7 illustrates four different measurements, where
A and B show examples on resolvable line pairs, while C
and D are not resolvable because two of the line pairs are
melted together. The linepairs are deemed to be not resolv-
able anymore when it is not possible to discern a black
line between two white pines or when the two of white
lines build up to a single local maxima instead of two local
maximas.
The results from the least resolvable line pairs measure-
ments on all source resolutions is plotted in Figure 8. At
the native resolution, the measured resolution is below the
native resolution, and the measured resolution increases
JERVELL HANSEN ET AL.7
FIGURE 7 Results from least resolvable linepair test. Horizontal source resolution is A, 4352. B, 5120. C, 5376. D, 5632
FIGURE 8 Horizontal measurement results from the least
resolvable line pairs experiment on a pixel-shifted projector with
WQXGA (2560) native resolution
steadily until the measured resolution reaches about 40%
above the native resolution.
When the source resolution reaches and goes beyond
double the native resolution, the measured resolution
drops down below the maximum measured resolution.
This is because the regular nature of the subframe genera-
tion is to handle the process as a case of upscaling instead
of downscaling.[12] Figure 1 illustrates that the resulting
pixel grids resolution is doubled in both horizontal and ver-
tical direction. Given the narrow nature of upscaling algo-
rithms, it is natural that one may lose single pixel details
when going above double the native resolution because the
sampling grid of both the subframes combined will then
possibly miss some single pixel details.
4.2 Grille contrast
The grille contrast measurement was executed as
described in section 3.2. In these measurements, the
source resolution is set to WQXGA, the native resolution
FIGURE 9 Grille contrast measurements for the source
resolution 3328 ×2080
of the projector, and then increased in steps of 10 up to
120% over native resolution.
Figure 9 shows the grille contrast measurement for
3328 ×2080 (30% over native resolution), and such a mea-
surement was obtained for all the given source resolutions.
The usage of such a curve is to look at the intersection point
between the desired contrast value and the contrast curve
of the display.
According to the IDMS, a typical desired contrast value
for displaying images is 25%, and extracting the measured
resolution for 25% contrast value gives us the measured
resolution curve shown in Figure 10.
The measured curve is monotonically increasing with
input resolution equal the source resolution as long as
the desired contrast is less than the measured contrast at
grille1 (single pixel width line pairs). When the measured
contrast at grille1 goes below the desired contrast, we start
to go up the contrast curve, and nrin Equation (1) goes
up. This leads to the measured resolution dropping at that
point such as at source resolution of 3580 in Figure 10.
8JERVELL HANSEN ET AL.
FIGURE 10 Resolution measurements versus source resolution,
given 25% contrast
Because the source resolution grid and the SLM res-
olution grid do not match each other in even numbers,
the source pixels may be represented by an uneven num-
ber of overlapping pixels in the projected image. This
means that the line pairs will sometimes be unevenly
represented, which again leads to uneven contrast mea-
surement between the different line pairs as shown in
Figure 11. When this occurs, the resolution measurement
is open for interpretation because the different line pairs
have different contrast ratios.
Figure 10 have used the biggest local line pair contrast
while Figure 12 shows how the resolution measurements
is when also using the smallest local line pair contrast
instead. Figure 13 illustrates examples of different local
contrast where Figure 13B have different contrast mea-
surements for the line pairs while Figure 13C show that
the first line pair is almost not detected.
4.3 Slanted edge
The slanted edge measurement was executed as described
in chapter 3.3. In these measurements, the source resolu-
tion is set to WQXGA, the native resolution of the projector,
and then increased in steps of 10 up to 120% over native
resolution.
As seen in Figure 14, the shifted edges are blurred
because of the overlapping pixels; Figure 15 shows that the
frequency response of the shifted images is lower than the
native unshifted edge.
The slanted edge MTF curve of each measurement is cal-
culated from the camera captured scenes, and the results
of these is presented in Figure 15.
5DISCUSSION
Increasing source resolution gives more details in the
source image to include in the subframes that makes up
the resulting projected image on the screen. There are sev-
eral different ways the subframes may be generated, but
the subframes are always more than one frame and are
always generated at the SLM resolution. So for the differ-
ent subframes to have different information in them, the
source resolution needs to be higher than the SLM resolu-
tion to provide enough details and information. Therefore,
it is intuitive that higher source resolution also results in
higher measured resolution.
But the shifted superimposition technique also has some
physical limitations. The optical overlap of the pixels as
shown in Figure 1 makes up the new and finer pixel grid,
but it also illustrates that these new pixels are not indepen-
dent of each other. Each resulting finer pixel in Figure 1
are made up of two overlapping SLM pixels from different
subframes, and each of these SLM pixels are also influ-
encing three other resulting pixels in the finer pixel grid.
This dependency makes the optical overlap function as a
low-pass filter, attenuating the highest frequencies of the
resulting image.
These physical limitations ensure that even though the
resulting resolution in the shifted superimposed image is
increasing with increasing source resolution, there must
be some limitations in how high resolution that may be
obtained. When counting the resulting pixels in the new
overlapping pixel grid shown in Figure 1, we see that the
number of separable pixels have doubled in both horizon-
tal and in vertical directions. But because of the inter-pixel
dependency each of these new pixels are not indepen-
dently controllable, and the low-pass filter behaviour of
the optical overlap will attenuate the highest frequencies.
These aspects affect the resulting resolution so that the
ideal double resolution will not be fully achieved.
The high frequency attenuation should be measurable,
so the method we use to measure the resolution will also
have an impact on the measured result. The least resolv-
able line pair method makes use of subjective observations
to see when the line pair is at the resolvable limit. The
idea here is that the resolution represents the amount of
separate distinguishable details, and to find this resolu-
tion number, we need to see how small details the display
is able to reproduce. This procedure is well known in the
industry and is widely adopted in some professional mar-
kets of projected display using the Johnson's criteria to
design and verify their display systems.[11] The least resolv-
able line pair method is often used as a system resolution
measurement rather than a display resolution measure-
ment, but there is no reason not to use this method also
as a pure display measurement. The results are dependant
JERVELL HANSEN ET AL.9
FIGURE 11 Images taken of the grille1 measurements for A, 3328. B, 3840. C, 4096
FIGURE 12 Resolution measurements versus source resolution,
given 25% contrast. This figure illustrates both the best case
measurement and the worst case measurement
on the performance of the source and the projected screen,
but the same can be said for the results from the other
measurement methods.
The grille contrast modulation measurements is
straightforward and not as open to interpretation when
the measurement results follow the criteria in the IDMS.
But this method will be open for interpretation when the
measured data behaves as shown in Figure 13B,C. The
problem with the data in Figure 13B is that the line pairs
have different contrast ratios, and the measurements will
be heavily dependent on which of these contrast ratios
is used. The reason for this difference in contrast is that
the pixel grid of the resulting pixels shown in Figure 1 do
not necessarily correlate to the pixel grid of the source
resolution. In these instances, rows and columns of the
source image will be represented by different geometric
compositions in the resulting pixel grid, as evidenced by
the different widths of the line pairs shown in Figure 11.
In Figure 11B,C, we see that the line pairs have different
widths, so the contrast measurements of these examples
will be of the nature in Figure 13B. In these cases, it is not
given which contrast to use, and the difference between
using the best and the worst line pair contrast is illus-
trated in Figure 12. There is a significant difference in
these resolution numbers, and it must be defined in such
cases how to interpret the contrast measurements when
the geometry of the line pairs are not consistent.
Figure 13C shows another interesting phenomena.
When the source resolution is closing in on double the
SLM resolution (and beyond), one may end up losing a
whole line. This is because the source resolution goes
above the resolution of the resulting pixel grid caused by
the pixel overlap, which is double the SLM resolution in
both horizontal and vertical direction. When the source
resolution goes above this limit, there are more details
represented in the source resolution than we have pixel
elements on the projected screen. So some of these details
will then be lost, and it is therefore possible to lose whole
line pairs. The least resolvable line pair test will disqual-
ify these results as one of the line pairs will be lost. But
the grille contrast modulation method will still calculate a
contrast ratio based on the remaining line pairs, and as we
see in the measured resolution in Figure 12, the measured
resolution actually goes up again at the higher resolutions
even though we are starting to lose a line pair in the Grille
measurements.
In Figure 11, we see three line pairs in both A, B, and C,
so all of these examples would pass the least resolvable line
pair test. In the grille contrast measurement however, both
figure 11B,C fall below 25% contrast and would therefore
not pass that measurement. This raises the question if 25%
really is a wise choice or if the target contrast should be
lower. In older applications, like CRT monitors for the pro-
fessional market, the target contrast limit was set between
2 and 10%,[11] so the 25% target contrast may seem a bit
too strict to measure the general resolution of a display.
It is good to have a target contrast if you have a specific
application that needs a given contrast to perform satisfac-
torily. But as a measurement for general resolution, this
method disqualifies details that are perfectly distinguish-
able just because the contrast does not reach this tests
desired contrast levels.
10 JERVELL HANSEN ET AL.
FIGURE 13 Grille plots of three different source resolutions: A, 2560. B, 3584. C, 5120
FIGURE 14 Slanted edge measurements at horizontal source resolutions A, unshifted 2560. B, 3584. C, 4352. D, 5376
The slanted edge measurement is a very good mea-
surement for optical performance, but as we see from
Figures 14 and 15, the shifted slanted edge does not change
significantly as a function of the input resolution. This
is logical because the source image in this case is a step
pattern that will be interpreted the same way in all of
these resolutions. This makes the slanted edge measure-
ment method an unsuitable method to measure the effect
of input resolution on a shifted superimposed display.
The least resolvable line pairs and the grille contrast
method both show that the measured resolution increases
with the source resolution up until approximately 40%
over the native resolution. The differences in the mea-
surement method give some differences in what source
resolution that gives the best measured resolution, but they
both indicate that the maximum gain of this resolution
enhancement method is around 40%.
The least resolvable line pair method measures the
smallest perceivable line/detail in the current configura-
tion, while the grille contrast method measures the con-
trast between neighbour lines/details in the image. So even
though both these methods agree on the maximum res-
JERVELL HANSEN ET AL.11
FIGURE 15 Slanted edge modulation transfer function (MTF)
calculations
olution gain of the shifted superimposition method, they
differ on the ideal source resolution. This is because of
the different features they analyse in the image, and the
ideal source resolution may differ depending of the applied
application and thus what definition of resolution is most
suitable for that specific use case.
Approximately 40% resolution increase also matches the
number of pixels actually projected on the screen, because
we are using two different subframes in two different posi-
tions for these measurements. With our WQXGA projector,
this gives us 2560 ×1600 ×2 number of pixels on the
screen. Keeping the aspect ratio, this will equal the num-
ber of pixels in a 3620 ×2262 image which is 41% (square
root of two) above the native resolution.
6CONCLUSION
The achieved resolution with the shifted superimposition
technique does increase as we increase the source reso-
lution. This is valid up to a certain threshold, where the
shifted superimposition method reaches its limit because
of the physical size of the projected SLM pixels and the
overlap of these pixels in different positions. The resolu-
tion enhancement limit seems to be about 40% above the
SLM resolution.
There are still open questions on how to measure this
resolution increase in the best way. We have utilized the
least resolvable line pair test, the grille contrast modula-
tion method, and the slanted edge method in this work.
All these methods have their shortcomings, but the two
best methods for this use case both measure a maximum
resolution increase at 40% while the slanted edge method
is found to be unsuitable for this measurement. The least
resolvable line pair method seems to be better suited to
measure the achieved resolution increase, because the
grille contrast modulation method takes too many assump-
tions on what attributes the measurements should have to
be defined as resolution.
ACKNOWLEDGMENT
This research is funded by the Research Council of Norway
under the BIA program, project HiLase 245569.
ORCID
Svein Arne Jervell Hansen https://orcid.org/
0000-0001-5781-9437
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12 JERVELL HANSEN ET AL.
AUTHOR BIOGRAPHIES
Svein Arne Jervell Hansen
received his master's degree
in electronics in 2007 at the
Norwegian University of Science
and Technology. Currently, he is
a PhD student at the University
of South-Eastern Norway, and he
is in addition to this working at Barco Fredrikstad
in Norway. His research is focusing on resolution
enhancement of projected displays.
Jon Yngve Hardeberg received
his MSc degree in signal processing
from NTNU, and his PhD in signal
and image processing from Ecole
Nationale Supérieure des Télécom-
munications in Paris, France. He is
a professor at the Norwegian Color
and Visual Computing Laboratory at the faculty of
computer science and media technology at NTNU in
Gjøvik. His current research interests include mul-
tispectral color imaging, print and image quality,
colorimetric device characterization, color manage-
ment, medical imaging, and cultural heritage imag-
ing, and he has coauthored more than 200 scientific
publications.
Muhammad Nadeem Akram
received his PhD in photonics
from Royal Institute of Technol-
ogy, Stockholm, Sweden, in 2005.
He is a professor at the Univer-
sity of South-Eastern Norway. His
research interests are semiconduc-
tor optoelectronics, vacuum electronics, imaging
optics, speckle reduction, laser projectors, and
human visual system modeling. He has published
more than 100 articles in scientific journals and
conferences
Howtocitethisarticle: Jervell Hansen SA,
Hardeberg JY, Nadeem Akram M. The effects
of source resolution on resolution enhancement
through shifted superimposition projection. JSocInf
Display. 2020;1–12. https://doi.org/10.1002/jsid.878
