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Abstract
A random method is presented to measure the modulation transfer function (MTF) of the rigid endoscope, evaluating its imaging quality. The experimental setup includes a four-dimensional (4D) mobile platform, a non-full-screen liquid-crystal display (LCD), three different kinds of patterns, a nasoendoscope of 0° direction of view under measurement, a complementary metal oxide semiconductor (CMOS) device, and a computer. The method is divided into three steps to complete the MTF measurement. First the geometric distortion is evaluated to determine the suitable sampling matrix (SSM) by the grid pattern. Then the illuminance inhomogeneity distribution is evaluated to obtain the illuminance compensation curve by the uniform grayscale pattern. Finally the MTFs are acquired by analyzing the spatial frequency contents of the compensated SSMs by the random patterns. By analysis and comparison, the method can improve the stability and accuracy for the MTF measurement in a simplified way.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Endoscopes are playing significant roles in medical field, and various kinds of them, such as nasoendoscope, cystoscopes, ureteroscopes, laparoscopes, laryngoscopes, arthroscopes and neuroscopes etc., are constantly emerging. With the advancement of modern computer technology, they become more and more popular in general surgical field. Instead of being directly observed by eyepiece, the images transmitted by them, can be captured by digital cameras and displayed on the computer screens for real-time inspection and diagnosis. Being long and slender optical device, they are widely used for minimal invasive surgery to examine the concealed cavities or hollow organs of the human body by natural or artificial made orifices. Thus it’s very important to evaluate the imaging quality for their successful application. Considering that endoscopes have small focal length and large field of view, the imaging quality of the central part is studied. For an endoscope, the theoretical resolution is defined by the formula [1–3]:
where λ is the wavelength of 650 nm, d is the working distance, and D represents the entrance pupil diameter. The theoretical resolution r (λ, d) is proportional to the ratio of the entrance pupil diameter D to the working distance d and its value is equal to 16.4 cycles/mm.The resolution test board is a traditional tool used in evaluating the imaging quality of endoscopes. It has square wave bar charts with a wide range of progressive increasing spatial frequency. Such as JBT 9328-1999 A1 [4] resolution test board, it is made up of 25 combined line unit charts with four different directions, each unit chart representing a different spatial frequency. Thus the specific chart image can be visually evaluated via eyes, where the spatial frequency of a poor contrast chart image is to be considered as the cutoff frequency of endoscopes. To decrease the experimental workload, a simplified resolution test board (Fig. 1) is designed, which is made up of 4 combined line unit charts with one direction, each unit chart representing a different spatial frequency from 3, 6, 9, 12 in cycles per mm. Theoretically, each contrast transfer function (CTF) value can be acquired by calculating the ratio of the output to input modulation depth which is the ratio of the subtraction of maximum and minimum value to the sum of maximum and minimum of the line unit image, according to the formula:
Neglecting higher harmonic components, Eq. (4) can be approximated from Eq. (3) as follows:
The main disadvantage of the resolution test board is the complexity and discreteness to measure CTF or MTF values. Although its design has been simplified to facilitate the measurement, the experimental operation is still a time-consuming and complicated movement or adjustment procedure. Because each line unit chart needs to be aligned and focused on the central part of the image to accomplish measurements for each spatial frequency. Finally the CTF or MTF values are measured only at certain discrete spatial frequencies and thus the total CTF or MTF curve has to be acquired by interpolation, which will introduce interpolation error into the CTF or MTF measurement.In addition, a lot of published literature [6–9] has concentrated on the lenses with well-corrected aberration to evaluate their imaging quality. Seldom literature has focused on the lenses with poorly-corrected aberration like endoscopes [10]. Our research objective is to present a method for evaluating the imaging quality of endoscopes in a simplified way. Thus three different kinds of patterns are prepared: a black and red grid pattern, a red pattern with a uniform grayscale and black and red random patterns with a flat spatial power spectrum. The remainder of this paper is organized into three sections. Section 2 describes the experimental device and design considerations. Section 3 demonstrates a random method to complete the MTF measurement in three steps. First the geometric distortion is evaluated to determine the suitable sampling matrix (SSM) by the grid pattern. Then the illuminance inhomogeneity distribution is evaluated to obtain the illuminance compensation curve by the uniform grayscale pattern. Finally the MTFs are acquired by analyzing the spatial frequency contents of the compensated SSMs by the random patterns. Based on the measured results, the analysis and comparison is demonstrated and the reliability is verified at two different working distances. Section 4 presents the conclusions.
2. Experimental setup
The experimental setup includes a 4D mobile platform, a non-full-screen LCD, a nasoendoscope of 0° direction of view whose entrance pupil diameter is 0.26 mm, a black and white CMOS camera and a computer, as shown in Fig. 2. The platform is used to control the movement of the installed LCD in four different dimensions, where it can move up and down within the range of 60 mm, right and left within the range of 25 mm, forth and back within the range of 25 mm and rotate within the range of 360°. The LCD consists of 1920 × 1080 pixels with pixel spacing of lLCD=57.6 μm, which stores and takes turns to display the patterns generated by computer in their original size. The CMOS has 1280 × 1024 pixels with pixel spacing of lCMOS=5.2 μm. The computer is used to analyze the output image and to display the processing result. The working distance d from the LCD to the entrance pupil of the nasoendoscope is 20 mm. The optical interface is used to convert the virtual image into the real image on the CMOS. Considering that the nasoendoscope is a low resolution device, in order not to affect the MTF measurement, the MTF of the optical interface should be high enough compared with the nasoendoscop to meet the experimental requirement.
In addition, according to the sampling theory, the highest spatial frequency of the pattern displayed on the LCD is fmax=1/(2 × lLCD×M) and the nyquist frequency of the CMOS is fN =1/(2 × lCMOS). To prevent aliasing, fmax ≤ fN should be ensured. Then based on the limitation, the magnification M is not smaller than 0.09.
3. MTF measurement
3.1 Alignment, adjustment, and nasoendoscope distortion characteristics
The LCD screen is adjusted to the appropriate brightness and moved longitudinally to the end of the nasoendoscope for the working distance of 20 mm. The optical adapter is adjusted to focus to the central part of the grid image. By rotating the platform, the experimental device can be aligned for both horizontal and vertical directions. Thus the center of the grid pattern is mapped to the center of the grid image and the central symmetric edges in the grid pattern are also centrally the grid image, as shown in Fig. 3.
From Fig. 3(b), the grid image is distorted gradually from the center to the edges, because the magnification decreases with the off-axis distance. The distortion of the image would increase error and uncertainty on the MTF measurement, thus the SSM size is indispensable for accurate MTF measurement. In both object and image planes, the center point is marked in green. The distance r, referring to the distance from the selected points to the center point, is normalized, where r = 1 represents the corners in object plane. F(r) represents the distances from the mapped points to the center point in the image plane. The relation between F(r) and r describes how the nasoendoscope distorts the grid image. Considering its axial symmetry, F(r) is measured only horizontally from the center to the right edge. The F(r) is obtained by interpolation and least-squares fitting, the distortion rate Δ(r)=(dF(r)/dr-1) is obtained by derivation of F(r) and the magnification M(r)=k(1+Δ(r)) is obtained by multiplying factor k which represents the central magnification relation between the object and the image planes and is equal to 0.192, as shown in Fig. 4. Thus the length of the non-distortion region (NDR) is L1=r*L and the width is W1=r*W, where L and W represent the horizontal and vertical distances and are both equal to 892 pixels in Fig. 3(b). Note that the size of the selected SSM is between 2r (λ, d) * 2r (λ, d) and NDR, that is between 33*33 and 45*45 pixels.
3.2 Illuminance analysis and compensation
The image illuminance caused by the nasoendoscope is inhomogeneous and decreases as the field angle increases. The illuminance inhomogeneity, shown in Fig. 5(a), will have certain effect on the MTF measurement. Here red region represents the NDR and green region represents the SSM. The illuminance distribution test is performed by using a uniform gray red pattern. After excising the background information in the output image, 10 frames of images are averaged. The gray value of each pixel of the average NDR is read to plot the three-dimensional (3D) illuminance distribution curve in Fig. 5(b), based on which the illuminance compensation can be performed on the random images.
Fig. 5. Illuminance distribution of output image: (a) NDR, SSM of the image and (b) 3D illuminance distribution for NDR.
3.3 MTF processing and result analysis
The random pattern with a size of 1080*1080 pixels (Fig. 6(a)), generated by a random number generator, has a flat spatial power spectrum distribution. Figure 6(b) represents the random image with the background information subtracted, where red square is the NDR and green square is the selected SSM. Note that the size of the selected SSM can affect the accuracy of the MTF measurement, thus the SSM close to the NDR is the better consideration.
The power spectral density (PSD) of the SSM in the horizontal direction is as follows:
The horizontal MTF is the ratio of PSD(vx)output to PSD(vx)in, then:According to the principle of measurement error and measurement uncertainty, 5-10 random images samples are generally average to reduce random errors in experimental measurements. The number of them below 5 will make the experimental results less convincing due to the insufficient samples and the number above 10 will bring about an increase in measurement time. Thus ten different random patterns are generated by the random number generator with 10 different initial seeds and ten NDRs of the corresponding ten random images are compensated by the illuminance compensation curve in Fig. 5(b).
Each vertical column is fourier transformed and added to columns to yield the horizontal PSDsoutput with the ten selected SSMs. After square rooting the horizontal PSDsoutput, a fourth-order polynomial curve for the mean MTF(νx) is plotted and modified by dividing the theoretical MTF of CMOS of MTFCMOS(νx)=sinc2(lCMOS*νx). Therefore, in the similar calculation way, the MTF(νy) for the vertical direction is also obtained. The measured results are shown in Fig. 7.
Fig. 7. MTF measurement results (d = 20 mm): (a) horizontal MTF comparison with different SSM sizes, (b) horizontal MTF comparison before and after illuminance compensation and (c) comparison with simplified resolution test board.
Figure 7(a) presents the effect of selecting different SSM sizes on the horizontal MTF measurement as an example. The sizes within the limited range (33*33 - 45*45) are in good agreement. However, above the limited range, the corresponding curves begin to fall, especially in the lower spatial frequencies. That is to say, beyond the limited range, geometric distribution would significantly affect the experimental results and bring about decreasing accuracy. Thus range limitation is essential to improve the accuracy of the MTF measurement.
Figure 7(b) presents the the horizontal MTF result as an example to study the effect of illuminance inhomogeneity on the MTF measurement. Due to the imaging characteristics of the nasoendoscope, only regions falling within the limited range of the images can be utilized. The small difference between the two curves shows that the MTF curve can be optimized to some accuracy after illuminance compensation.
Figure 7(c) presents the comparison results with the simplified resolution test board at spatial frequencies of 3, 6, 9, and 12 cycles/mm. The results show that the random method in a greatly simplified way yields the consistent results than the traditional method in a much more complicated way. That is to say, it’s necessary to make four alignment adjustments to obtain four discrete spatial frequencies by using the simplified resolution test board. However, for the random method, only one alignment is required to get a total MTF curve. Thus reducing the numbers of alignment adjurement can improve the stability of the MTF measurement.
Finally, when the working distance d is 25 mm, the comparison with the simplified resolution test board is in good agreement in Fig. 8.
4. Conclusions
A random method and an experimental setup is demonstrated for the MTF measurement of the nasoendoscope. The method includes 3 different kinds of patterns, and the setup includes a 4D mobile platform, a LCD, a nasoendoscope of 0° direction of view, a CMOS camera, and a computer. Based on the grid output image, the geometric distortion is evaluated to determine the SSM. The inhomogeneous illuminance distribution is evaluated to determine the illuminance compensation. The MTFs are obtained by analyzing the spatial frequency contents of the SSMs compensated of the random images.
The main advantage of the method is to provide a new solution for the imaging evaluation of endoscopes. It improves the experimental accuracy by determining the SSM range and illuminance compensation. It improves the experimental stability to obtain total MTF curves in a simplified experimental operation by reducing frequent alignment.
The important factor affecting the experiment is the choice of LCD screen. The full-screen LCD can introduce a significant amount of aberrations (principally due to lack of flatness of the front flats) and bring about additional error to experimental measurement. Thus a non-full-screen LCD with a more matrix size and a smaller pixel spacing, presenting better uncorrelated random patterns, would provides a sufficient guarantee for the successful completion of the experimental measurement.
Acknowledgments
We thank Mr Wu Wanzhe, as well as the Hubei Huazhong Photoelectric Technology Corpration for the access to their devices.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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