Introduction

In recent medical image diagnosis, liquid crystal displays (LCDs) have mostly been adopted as the main display devices, and they are playing an important role due to their excellent resolution property, high maximal luminance, and space-saving characteristics. The remarkable higher resolution [1, 2] than that is provided by the cathode ray tube (CRT) display is the most important feature of the LCDs. However, their noise properties seemed not to be good, as described in recent papers [2–4]. Moreover, the method of evaluation of the noise property is not well-defined because of problems in the treatment of signal components generated from discrete and complicated pixel structures. Also the accuracy of the evaluation results has not been discussed sufficiently.

Figure 1 shows close-up images of a uniform area and bar patterns with one pixel width, displayed on a 3-mega-pixel (MP) monochrome LCD in portrait orientation. As shown in this figure, the pixels are spaced by the dark separators that consist of electric lines and other opaque materials; the luminance distribution emitted from the pixels is microscopically periodic according to such a pixel structure. This feature differs fundamentally from the digital radiographic image data which are analyzed by means of well-defined noise power spectrum (NPS) measurement methods such as an International Electrotechnical Commission (IEC)-recommended method. Therefore, consideration of the periodic components is essential in the NPS evaluation of the LCDs.

Fig. 1
figure 1

Close-up images of (a) a uniform area and (b) bar patterns with one pixel width, displayed on a 3-MP monochrome LCD in portrait orientation. Each pixel consists of three sub-pixels in a two-domain

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Recent researchers employed common measurement procedures for the NPS measurement of LCDs, in which LCD images were captured digitally by cameras with charge-coupled devices (CCD), and a two-dimensional (2D) fast Fourier transform (FFT) was used [2–4]. In addition, pixel-aligned numerical apertures (PAs) that average the CCD data within the area corresponding to one LCD pixel were commonly applied for evaluation of the noise property, which was separated into inter- and intra-pixel variations. However, it is clear that the method using the PA cannot evaluate the luminance variation caused by parts finer than one pixel, such as the sub-pixels included in one pixel [2, 3]. Moreover, the researchers did not present enough valuable NPS results for the common 2D FFT methods without the use of PA. In the NPS results, some spectral leakage errors and the bad influence of insufficient frequency resolution were included. Thus, the results of the PA analysis were not effective with respect to the comprehensive evaluation of the noise property.

Saunders et al. [3] presented the most reliable NPS results for three medical LCDs. They analyzed the NPS by using 256 × 256 CCD data segments which is pre-processed by a Hanning windowing. The windowing process is generally employed for reducing spectral errors due to spectral leakage in the Fourier analysis, which is generally caused when the periodic signal component (the pixel structures in the LCD case) was analyzed with the data range not coinciding with the exact signal cycle. Although the windowing process is effective for spectral leakage, it is well known that it causes unavoidable degradation of the frequency resolution. Therefore, Saunders et al. presented results with recognizable errors that were caused by overlapping of adjacent frequency peaks that were deformed into the round shapes by the degradation of the frequency resolution.

Our purpose in this study was to investigate the optimal NPS measurement method that enables a comprehensive analysis of the LCD’s noise, including the effect on the pixel structures. If the periodic components from the pixel structures can be analyzed correctly, their frequency peaks should appear as sharp spikes in the NPS curve, and consequently the random signal components from the inter- and intra-pixel variations can be expressed as the regions between the sharp spikes. Therefore, without the use of PA analysis, a comprehensive analysis will be possible by the use of correctly obtained NPSs. In order to achieve this, it is necessary to find an optimal analysis method with higher frequency resolution and reduced spectral leakage errors, compared to earlier methods proposed in the recent papers.

We investigated the methods that employ 2D FFT methods (2D methods) by the use of 256 × 256, 512 × 512, and 1024 × 1024 CCD pixel segments and a 1D FFT method (1D method). The 2D methods using 512 × 512 and 1024 × 1024 pixel segments were employed for the improvement of the frequency resolution for the 256 × 256 pixel segment. The 1D method using 1D noise profiles with 1024-point data obtained by numerical slit scanning for the CCD data was also compared with the 2D methods. In these methods, a background trend correction (BTC) and a Hanning windowing process as the pre-processes for the CCD data segments were investigated with regard to their effectiveness.

Materials and methods

LCDs and camera description

The LCDs that we employed were a 3-MP monochrome LCD (ME351i, Totoku, Tokyo, Japan), a 5-MP monochrome LCD (ME551i, Totoku, Tokyo, Japan) and a prototype 5-MP monochrome LCD (ME551i base) equipped with a newly developed anti-reflection (AR) surface-coated panel. We adopted the AR surface instead of an anti-glare (AG) surface in order to improve the reflection property and remove the harmful influences of the AG such as an increase of the black level and additional noise caused by its light diffusion. In the measurements, all displays were configured in the portrait orientation. A high-resolution single-lens reflex-type digital camera (D80, Nikon, Tokyo, Japan) that consists of a CCD sensor with 3872 × 2592 pixels and 12-bit pixel depth was employed for capturing the displayed image. The camera was equipped with a close-up lens (Nikon Micro-Nikkor 60 mm F2.8D) for obtaining close-up images. In this study, we employed normalized NPS for the noise evaluation in accordance with Ref. [1]. Thus, for the NPS measurement, it was important that the camera had an exact linear characteristic curve of luminance versus the CCD pixel value. We confirmed that the camera employed in this study had good linearity in the range of 0.2–700 cd/m2 by using a luminance meter (LS-110, Konica Minolta, Tokyo, Japan) and uniform square patterns displayed on the LCD with a 0–100 % digital drive level (DDL).

Figure 2 shows the experimental setup. A uniform image with a 50% DDL, including two white level vertical lines with a horizontal interval of 100 display pixels, was displayed on the LCDs. The 50% DDL provided a luminance of about 50 cd/m2 in a luminance characteristic of a Grayscale Standard Display Function (GSDF) in a Digital Imaging and Communications in Medicine (DICOM) standard. The two lines were used for calibrating the CCD pixel number per one display pixel, so that the real frequency scale on the display surface could be calibrated. The uniform area including the two lines was captured by the use of digital camera, and then the 1024 × 1024-pixel area for evaluation (parent area) was extracted from the center of the CCD data (Fig. 3). When the camera captured the displayed image by the minimal available distance between the camera lens and the display, the captured area was set to approximately 22 mm × 14 mm as the narrowest area. With this setup, the sampling pitch on the display surface reached 0.0056 mm, so that the aliasing errors became avoidable because of the very high Nyquist frequency of 89 cycles/mm. We selected a small lens aperture with an f-stop of f/11 to ensure that the camera had a relatively large depth of field, which allowed objects near the true focal plane also to be captured with relative sharpness.

Fig. 2
figure 2

Experimental setup with a high-resolution single-lens reflex-type digital camera (D80, Nikon) equipped with a close-up lens (Micronikkor 60 mm F2.8/D, Nikon)

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Fig. 3
figure 3

The uniform area including the two white level lines captured by the use of camera. The center 1024 × 1024 CCD pixels area for evaluation, as indicated by a dotted box

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NPS measurement

We employed the 2D method by using 256 × 256-pixel segments as the basic method for comparison with the other experimental methods. In order to apply an IEC 62220-1-recommended method for digital X-ray detectors, we obtained the x- and y-NPS results by band-averaging at each frequency with the use of ±7 points on either side of the u- and v-axis (corresponding to the x- and y- axis in the spatial domain) and one point on each axis, in order to reduce the Fourier transform fluctuation for the random signal. Although the IEC-recommended method excludes the axis data for reducing the effect of the unneeded periodic components, in this study, we included the axis data on purpose to evaluate the periodic signal from the pixel structures simultaneously. In the basic method, we applied a BTC by the use of a 2D second-order polynomial background fit as a pre-process for the segment, and we then computed the final NPS per image by averaging non-overlapped 16 256 × 256-pixel segments extracted from the parent area. Before the experiments, we measured the camera’s inherent NPS to relate the noise levels to the experimental errors of the image acquisition. In order to measure the inherent NPS, we captured a uniform light source with the same luminance as the LCD images by the camera, and we then analyzed the NPS by using the basic method.

In the investigation of the basic method, we examined the efficacy of the Hanning windowing process. Then, methods using 512 × 512 and 1024 × 1024 pixel segments were compared with the basic method. The final NPSs for 512 × 512 pixels were computed by averaging of four segments, and for 1024 × 1024 pixels there was no choice but to use only one segment because of the size of the parent area. In these two methods, the segments were processed by the use of both the BTC and Hanning windowing.

Also, we examined a 1D FFT method by using 1024-point noise profiles. The noise profile was obtained by scanning of the parent area by the use of a numerical synthesized slit that averages 60 pixels in the direction perpendicular to the scanning direction. The pixel number of the numerical slit was determined experimentally as a minimal pixel number which could approximately extract a center slice of the 2D NPS [5, 6]. Within the parent area, 25 noise profiles were obtained, and the final NPSs were calculated by averaging of their 1D NPSs. Each 1D noise profile was processed by a BTC with the use of a 1D second-order polynomial fit and Hanning windowing.

Results

Figure 4 shows results of the camera’s inherent NPSs in the x and y directions. The camera provided a sufficiently low noise level for the NPS measurement. Figure 5 shows comparisons of the resultant NPSs of the basic method for the ME351i. In both x and y directions, the results obtained by the use of only the BTC provided significant errors due to the spectral leakages. By combining the Hanning windowing process with the BTC, the spectra in which the spectral leakage errors were corrected could be obtained, but unacceptable degradation of the frequency resolution was evident from the broad spectral peaks.

Fig. 4
figure 4

The camera’s inherent NPS measured from the uniform light source. The noise level of the camera was sufficiently low for the NPS evaluation

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Fig. 5
figure 5

NPS results of the basic method for the ME351i. In both (a) x and (b) y direction, the results obtained by the use of only the BTC provided significant errors due to spectral leakages

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Figure 6 shows a comparison of the results for the 512 × 512 and 1024 × 1024-pixel segments and for the 1D method. The measurements were performed for the ME351i (x and y direction) and the ME551i (x direction only). The frequency resolution for 512 × 512-pixel segment was not sufficient for evaluating the NPS in the regions including adjacent peaks, and it caused errors especially in the low-frequency range. Although the method with 1024 × 1024-pixel segment presented a better frequency resolution, as did the 1D FFT method, the method caused a rise in the spectrum near zero frequency, which indicated insufficient BTC for the 1024 × 1024-pixel segment.

Fig. 6
figure 6

Comparisons of NPS results for the 512 × 512 and 1024 × 1024-pixel segments and for the 1D method by the use of 1024-point 1D noise profile, in the (a, b, c) x and (d, e, f) y direction for ME351i, and (g, h, i) x direction for the ME551i. The 1D method provided the most reliable results

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The 1D FFT method provided the most reliable results among all methods because of the successful BTC and the better frequency resolution.

Figure 7 shows a comparison of the NPSs for the ME551i and the prototype 5-MP LCD, in which the difference between these two LCDs was only in the surface architecture. In this comparison, we employed the 1D method. As shown in the figure, it was clear that the AR coating improved the noise property significantly.

Fig. 7
figure 7

Comparison of the NPSs in the (a) x and (b) y direction for the ME551i with an AG surface and the prototype 5-MP LCD with the new AR surface. The AR-coated surface improved the noise property significantly

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Discussion

For the experiment in which we used the basic method using 256 × 256-pixel segment, it was confirmed that applying the Hanning windowing process was very useful for reduction of spectral leakage errors. We examined various windowing processes in a preparatory investigation. From the results, it was confirmed that the windowing process, which could suppress degradation of the frequency resolution, did not provide a sufficient reduction of the spectral leakage errors. Because the spectral leakage did serious damage to the noise level evaluation, the Hanning windowing, which provided excellent reduction of the frequency leakage, was most suitable. If the windowing process was not applied, the frequency peaks from the pixel structures changed into frequency distributions with a widespread chevron shape, as shown in Fig. 5. When the tails of adjacent distributions overlap each other, the NPS values between the peaks become impossible to evaluate. Thus, the Hanning windowing process was very important for accurate NPS estimation. However, because the frequency resolution of the FFT analysis by the use of 256 × 256 pixels was not sufficient originally, the resolving of the adjacent frequency peaks became impossible because of the degraded frequency resolution caused by the windowing process.

A rise of the NPS values near zero frequency was observed in the result obtained with the basic method. This indicated that the BTC process was not effective for the 2D method in spite of the narrow area of the 256 × 256 pixels. Although the luminance distribution of the evaluated area looked quite uniform, it actually did not have the simple non-uniformity that is correctable by the BTC. In order to improve this, we recalculated the NPS by using the higher order polynomial fits, but the problem was not resolved effectively.

The method of using 512 × 512-pixel segments also did not provided sufficient frequency resolution. In the NPS results, the low-frequency region that had several peaks with close frequencies could not be evaluated correctly. For the method of using 1024 × 1024 pixels, the frequency resolution was adequate for the NPS evaluation. However, the BTC issue which causes the NPS to rise near zero frequency remained.

The 1D method of using 1024-point noise profiles provided the most acceptable results, although some fluctuations of the NPS values over the entire frequency range were present in spite of the averaging of NPS results for 25 1D noise profiles. However, even if a more accurate NPS is demanded, averaging of multiple NPSs obtained by many capturing is not effective because the target of the NPS is non-stochastic spatial noise [2]. Therefore, we considered that smoothing techniques applicable to waveforms including many peaks would be effective.

From the results shown in Fig. 6, we could compare the NPSs of the x and y direction for ME351i and also compare the x-directional NPSs of ME351i and ME551i. In the comparison of the x- and y-directional NPSs, almost the same baseline level between the two curves, which express the same random noise level, was presented. The results suggested that the random noise components of ME351i might be a nearly isotropic. The different spectral peaks between the two curves indicated the actual spectral difference between the x and y directions, which were caused by the complicated pixel structures shown in Fig. 1. For the comparison of ME351i and ME551i, the baseline level of ME551i in a frequency range below 10 cycles/mm was slightly higher than that of ME351i. Actually, we could perceptually recognize a slight difference in the amount of noise with a fine granularity. Since ME351i and ME551i were equipped with different AG surfaces, this result led to our presumption that the difference between the two LCDs was caused by a difference in the materials that form respective AG surfaces.

The prototype 5-MP LCD equipped with an AR-coated panel provided excellent noise properties. When we examined the AG surface of ME551i by using a magnifying glass, we were able to find a very fine granularity. In general, the AG forms a microscopic granulated surface in order to diffuse the reflection, and unfortunately its microparticles diffuse a part of the transmitted light from each liquid crystal. Therefore, it is considered that the light diffusion causes the additional noise. On the other hand, because the AR surface achieves anti-reflection by utilizing the optical phase change upon reflection by using very thin AR layers, the surface does not consist of any granulated structures, and therefore does not generate any additional noise similar to the AG surface. Actually, for the prototype 5-MP LCD, we were not able to find the granularity that was observed in the AG surface. Therefore, the AR-coated panel will be effective for improving the quality of displayed images, because of its better noise property and the anti-reflection performance. The comparison of the ME551i and the prototype 5-MP LCD proved that the 1D method can yield enough valuable NPS results, including a great deal of information on the complex noise components with various frequencies.

Conclusion

We investigated NPS analysis methods for medical monochrome LCDs. Our study showed that a method of using 1D FFT and combining the background trend correction with the second-order polynomial fit and the Hanning windowing process was effective. With this method, a comprehensive noise evaluation that included periodic components of the pixel structure became possible. Therefore, noise property estimation by the use of this method is useful in understanding and quantifying the performance of LCDs.