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Abstract
This study examines the constraints in measuring the contrast modulation or line-pair luminance modulation for pixelated displays. Simulation results show that measurement precision is affected by the offset between the display pixels and the detector array of the light measuring device (LMD). The contrast modulation is underestimated if the spatial imaging performance of the LMD is inadequate. A high pixel ratio, i.e., the number of pixels of the measurement device per display pixel interval, is required to increase the measurement accuracy. However, determining the minimum required pixel ratio is not straightforward, as the accuracy depends on the display device architecture as well.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrahigh definition (UHD) technology produces visually realistic digital images [1]. UHD devices are usually categorized by the horizontal pixel counts of the standard image formats of their input/output signals, such as 4K and 8K. However, the spatial imaging performance of a display is typically not determined solely by the pixel count. Although traditional flat panel displays with R (red), G (green), and B (blue) stripe patterns use separate RGB micro-color-filter elements within each pixel, some recent display technologies do not use the three colors for each incoming image pixel, thus obscuring the pixel count [2]. Furthermore, the optical elements used in a display structure affect the spatial imaging performance of the display. For example, a diffusing film can be overlaid on the front surface of a panel to improve the panel’s viewing angle and reduce the specular reflection of ambient light. However, front surface diffusers generate interpixel crosstalk and sparkle, thereby degrading the spatial resolution characteristics of the display as shown in Fig. 1.
Fig. 1. Grille patterns displayed on two 4K displays (a) without and (b) with a front surface diffuser.
The spatial resolution characteristics of a display are measured using the Michelson contrast of the luminance values of the displayed white and black lines of an alternating line-pair pattern, which is called grille pattern (Fig. 1). The luminance modulation of the grille pattern, i.e., the contrast modulation, is a historical display characteristic index or definition that dates from the days of the cathode-ray tube. The International Committee for Display Metrology (ICDM) recommends measuring the contrast modulation [3–6]. The Consumer Technology Association (CTA) in the USA also uses a minimum required contrast modulation of 50% as an industry benchmark for 8K UHD displays [7].
Contrast modulation is measured from an image of a displayed grille pattern, which is captured by a light measuring device (LMD) with a digital area sensor. The black and white luminance values are obtained from the captured image by averaging the sampled luminance values within the display pixel width for each line, wherein the display pixel is defined in the image format of the display input signal and not by the physical pixel and architecture of the display devices. For example, the pixel count and sampling lattice for the 4K and 8K UHD formats are defined in ITU-R Recommendation BT.2020 [8].
It is well-known that the contrast modulation is affected by the limitations of the spatial imaging performance of the LMD. Therefore, the grille pattern must be captured at a relatively high magnification to prevent the contrast modulation estimation from being underestimated by the LMD. The ICDM recommended over 10 [3] (and preferably over 20 [4]) LMD pixels per display pixel. In 2016, the ICDM raised the minimum required pixel ratio to an empirically determined value of 30 [5]. The basis for these criteria remains unclear. This study demonstrates the accuracy and precision limitations of the contrast modulation method in a quantitative manner using simulations.
2. Simulation
2.1 Contrast modulation method
First, a grille pattern is displayed on a screen and captured by an LMD. The alternating black and white lines are aligned to the sampling array of the LMD. The luminance values of the captured image are averaged along the lines to yield a one-dimensional luminance profile. To obtain the average luminance values within the display-pixel-wide lines, a moving window average filter (MWAF) [4] is applied to the profile. The MWAF is designed as a box filter with an integer length that approximates the aforementioned pixel ratio, i.e., the number of pixels in the LMD output image accommodated within a single sampling-grid interval of the display input image. The maxima and minima of the filtered profile represent the luminance values of the black and white lines, respectively. Finally, the Michelson contrast of the luminance values of the black and white lines is calculated.
In practice, a grille pattern with a non-integer pixel ratio is usually captured, and this ratio is rounded off to the nearest integer in the final MWAF design. However, this rounding results in an error that biases the contrast modulation estimation. Furthermore, the precision of such measurements is affected by the offset between the display pixels and the detector array of the LMD.
2.2 Simulation conditions
To examine the accuracy and precision of the contrast modulation measurement, simulations were performed assuming a model display with RGB subpixels and a model LMD.
The model display was assumed to have an RGB subpixel layout. Figure 2(a) illustrates a single black mask-less pixel. The luminance ratio of the RGB subpixels was set to 0.2:0.7:0.1. This ratio was determined by rounding the ratio of the luminance values of the sRGB primaries (0.2126:0.7151:0.0722) to the first decimal place. The horizontal luminance profile LRGB(x) was normalized so that the white luminance becomes unity, i.e., $\int\nolimits_{0}^{1}$LRGB(x)dx = 1, and LRGB(x) is given as
Fig. 2. RGB subpixel layout with 1/3-pixelDISP-wide micro-color filters: (a) single pixel image and (b) luminance profile.
The model LMD was assumed to output 2D sampled image data. The pixel interval was defined by a square sampling grid. The LMD was assumed to have a modulation transfer function (MTF) of |sinc(ξxLMD, ξyLMD)|4 to represent typical camera MTFs [9,10], where ξxLMD and ξyLMD are horizontal and vertical spatial frequencies in cycles per LMD pixel (pixelLMD), respectively. The reason is that a photodetector having a 100% fill factor, i.e., a square spatial sensitivity, has an MTF of |sinc(ξxLMD, ξyLMD)|. For computational simplicity, the optical system in front of the photodetector was assumed to have a sinc-based MTF such that the line spread function LSFLMD(xLMD) was calculated as a rectangular function convolved three times with itself as rect(xLMD) ⁎ rect(xLMD) ⁎ rect(xLMD) ⁎ rect(xLMD). The LSFLMD(xLMD) becomes zero for |xLMD| > 2 because rect(xLMD) ranges from −0.5 to 0.5. Figure 3 shows the typical MTFLMD(ξxLMD) of |sinc(ξxLMD)|4 and the corresponding LSFLMD(xLMD).
2.3 Effect of pixel offset on precision
The luminance profile obtained from an image captured by an LMD, LSFLMD, is affected by the sampling phase, as illustrated in Fig. 4, in the case of a pixel ratio of 5. Herein, the offset X is defined as the distance in pixelLMD from the left-side boundary of the display pixel to the nearest sampling position of the LMD pixel, as shown in Fig. 4(a). The gray patches shown in Fig. 4(a) represent the luminance levels of the LMD pixels sampled at X/5 + P/5 in pixelDISP, where P is a variable integer. X ranges from −0.4 to 0.5 at intervals of 0.1 in pixelLMD. The luminance LLMD(x) was computed by the convolution of LRGB(x) and LSFLMD[5(x – X/5 – P/5)]. Figure 4(b) shows the LLMD and values applied with a 5-pixelLMD-wide MWAF, LMWAF. Figure 4(c) shows the peak values of the MWAF-applied luminance profile, PRGB, as a function of X. The values are below the white luminance level, i.e., the maximum value (1), in the vertical axis because of the low pixel ratio. Furthermore, the values are slightly different among the offset values.
Fig. 4. Luminance profiles calculated at a pixel ratio of 5 with offsets from −0.4 to 0.5 at intervals of 0.1 pixelLMD: (a) Sampled gray patches for each offset, (b) normalized luminance profiles with and without applying an MWAF, and (c) the peak value of the MWAF-applied luminance profile as a function of offset X. Orange and brown circle markers indicate the sampling positions.
2.4 Effect of pixel ratio on accuracy
The MWAF is designed to have an integer tap length that is equal to the nearest integer of the pixel ratio [4]. This rounding error affects the measurement accuracy. Figure 5 shows the peak values of the MWAF-applied luminance profiles (PRGB) calculated at pixel ratios, M, ranging from 5 to 35 at intervals of 1. This includes non-integer pixel ratios of M ± 0.1 and M ± 0.2. The LMD pixel offsets (X) varied from −0.4 to 0.5 at intervals of 0.1 pixelLMD for each pixel ratio. When the pixel ratio increases, the results approach the white luminance level of 1. The peak value is underestimated by approximately 1% when the pixel ratio is 30.
Fig. 5. Peak values of the MWAF-applied luminance profiles calculated at integer pixel ratios M from 5 to 35 in addition to M ± 0.1 and M ± 0.2. The LMD pixel offsets (X) varied from −0.4 to 0.5 at intervals of 0.1 pixelLMD for each pixel ratio.
2.5. Device architecture dependency
The accuracy and precision of the contrast modulation estimation depend on the device architecture. To demonstrate this dependency, an RGB subpixel arrangement having a black mask on both sides of each subpixel was used instead of the arrangement shown in Fig. 2. Furthermore, the black mask width was set to 1/10 of the pixel width to simulate typical UHD displays with a simple fraction, that is, the width ratio of the micro-color filter to the black mask was 2:1. The horizontal luminance profile LRGB+MASK is expressed as
Fig. 6. Simulation of contrast modulation for a display with an RGB subpixel arrangement with a black mask: (a) subpixel arrangement and (b) peak values of the MWAF-applied luminance profiles at integer pixel ratios M and non-integer pixel ratios of M ± 0.1 and M ± 0.2, with LMD pixel offsets at intervals of 0.1 pixelLMD.
A black-masked RGB subpixel arrangement having a diffuser was also used in this simulation. The diffuser was assumed to be a display-pixel-wide rectangular averaging filter, rect(x). The horizontal luminance profile LRGB+MASK+DFUS is expressed as
where $\int\nolimits_{0}^{1}$LRGB+MASK+DFUS(x)dx = 0.875. The diffuser was determined to simulate a display that met the CTA criterion, using a simple function. The luminance value of the black line in the grille pattern was then calculated as 1 − 0.875 = 0.125, and the contrast modulation was 0.75 (> 0.5). Figure 7(a) compares the luminance profiles of the RGB subpixel arrangement with and without the diffuser. Figure 7(b) shows the peak values of the MWAF-applied luminance profiles with the diffuser (PRGB+MASK+DFUS) obtained using the same pixel ratios and LMD pixel offsets as those of Fig. 6(b). A higher pixel ratio is needed to obtain more accurate results.Fig. 7. Simulation of contrast modulation for a display with the black-masked RGB subpixel arrangement: (a) luminance profile of the display pixel with and without the diffuser and (b) peak values of the MWAF-applied luminance profiles with the diffuser at integer pixel ratios M in addition to non-integer pixel ratios of M ± 0.1 and M ± 0.2, with LMD pixel offsets at intervals of 0.1 pixelLMD.
2.6. Correction of contrast modulation estimation for non-integer pixel ratios
The ICDM provides an optional method of improving the accuracy of the contrast modulation estimation for non-integer pixel ratios [5]. The contrast modulation at a non-integer pixel ratio m is interpolated with the weighted average of two luminance values using two MWAFs: one has a length of ⌈m⌉, whereas the other one has a length of ⌊m⌋, where ⌈m⌉ and ⌊m⌋ indicate the round-up and -down values of m, respectively. Figure 8 shows the interpolated PRGB calculated for the black mask-less RGB stripe pattern (Fig. 2) at pixel ratios ranging from 5 to 35 at intervals of 0.1, with LMD pixel offsets at intervals of 0.1. The interpolated Lpeak values for the non-integer pixel ratios have significantly better continuity with those for the integer pixel ratios than the Lpeak values computed using MWAFs with the lengths of the rounded-off pixel ratios (Fig. 5), although they are slightly waved because of the rough weighted average interpolation.
Fig. 8. Peak values calculated for the black mask-less RGB stripe pattern (Fig. 2) of the luminance profiles with the correction for non-integer pixel ratios at intervals of 0.1. The LMD pixel offsets at intervals of 0.1 pixelLMD.
3. Discussion
Contrast modulation is not a measure of sine- or square-wave-derived modulations. A measure of contrast modulation indicates only the interpixel crosstalk. Since the convolution theorem is not applicable to contrast modulation, the result is an underestimation of contrast modulation at low pixel ratios.
Because the accuracy depends on the display device architecture and MTF of the LMD, it is a big challenge to determine the minimum required pixel ratio. Although this study mainly focused on RGB stripe subpixel patterns, many modern displays utilize subpixel arrangements wherein the subpixel density depends on the subpixel type or color. Examples include the Pentile layout used primarily in mobile devices (green subpixels have higher density compared to red and blue) and the “M+” layout used in TVs. Their contrast modulation would depend on the color, impacting the accuracy and precision, the analysis of which will be very complex. A practical approach for increasing accuracy in measuring contrast modulation is to identify a pixel ratio that allows the contrast modulation to reach a plateau while still considering precision. However, a high pixel ratio usually results in a short shooting distance, where reflections from the objective lens back to the display and stray light within the optics of the LMD can introduce considerable errors [2].
Unlike the contrast modulation measurement, the display MTF measurement can compensate for the MTF of the LMD. The advantage of MTF is that the spatial imaging performance of an imaging system can be analyzed by multiplying the MTFs of the subsystems in the frequency domain based on the convolution theorem instead of repeatedly convolving their impulse responses in the spatial domain. A line-based display MTF measurement method accurately computes the MTF for a wide range of pixel ratios [11].
4. Conclusions
In this study, the fundamental limitations of measuring contrast modulation were revealed. It was found that the contrast modulation method includes errors owing to the offset between the display pixels and the sampling positions of the LMD. Furthermore, the contrast modulation was significantly underestimated owing to the spatial resolution performance of the LMD when the pixel ratio is low. In practice, a high pixel ratio is empirically determined to achieve an accuracy that depends on the MTF of the LMD and the display device architecture. Evidently, it is a metrological and methodological issue that the convolution theorem is not used in the contrast modulation method. The line-based MTF measurement is recommended to more accurately characterize the spatial imaging performance of displays for a wide range of pixel ratios.
Acknowledgments
I thank Dr. K. Käläntär of Global Optical Solutions (Japan) and other eminent experts at the ICDM and IEC TC 110 for their fruitful discussions.
Disclosures
The author declares no conflicts of interest.
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