Phase transfer function based method to alleviate image artifacts in wavefront coding imaging system

Wavefront coding extended the depth of field to a great extent with simpler structure compared to confocal microscope. With cubic phase mask (CPM) employed in the STOP of the objective lens, blurred images will be obtained in charge coupled device (CCD), which will be restored to sharp images by Wiener filter. We proposed that one CPM is used in one microscope although there are different objective lenses with different power indices. The microscope proposed here is the wavefront coding one when the CPM is used in the STOP; while it is the traditional one when a plane plate is used in the STOP. Firstly, make the STOP in the last surface of the lens, and then add a plane plate at the STOP with the same material and the same center thickness of the CPM. Traditional objective lenses are designed, based on which wavefront coding system will be designed with the plane plate replaced by a CPM. Secondly, the parameters of CPMs in different objective lenses are optimized to certain ranges based on metric function of stability of modulation transfer function (MTF). The optimal parameter is chosen from these ranges. A set of objective lenses is designed as an example with one CPM. The simulation results shows that the depth of field of 4X, 10X, 40X, 60X and 100X objective lenses with the same CPM can reach to 400um, 40um, 24um, 16um and 2um respectively, which is much larger than 55.5um, 8.5um, 1um, 0.4um and 0.19um of the traditional ones.

In the space limited infrared imaging system based MEMS, the adjustment of optical readout part is inconvenient. This paper proposed a method of wave-front coding to extend the depth of focus/field of the optical readout system, to solve the problem above, and to reduce the demanding for precision in processing and assemblage of the optical readout system itself as well. The wave-front coded imaging system consists of optical coding and digital decoding. By adding a CPM (Cubic Phase Mask) on the pupil plane, it becomes non-sensitive to defocussing within an extended range. The system has similar PSFs and almost equally blurred intermediate images can be obtained. Sharp images are supposed to be acquired based on image restoration algorithms, with the same PSF as a decoding core.We studied the conventional optical imaging system, which had the same optical performance with the wave-front coding one for comparing. Analogue imaging experiments were carried out. And one PSF was used as a simple direct inverse filter, for imaging restoration. Relatively sharp restored images were obtained. Comparatively, the analogue defocussing images of the conventional system were badly destroyed. Using the decrease of the MTF as a standard, we found the depth of focus/field of the wave-front coding system had been extended significantly.

A novel anti-cat-eye effect imaging technique based on wavefront coding is proposed as a solution to the problem of previous anti-cat-eye effect imaging techniques where imaging quality was sacrificed to reduce the retroreflection from the photoelectric imaging equipment. With the application of the Fresnel–Kirchhoff diffraction theory, and the definition of generalized pupil function combining both phase modulation and defocus factors, the cat-eye echo formation of the wavefront coded imaging system is theoretically modeled. Based on the physical model, the diffracted spot profile distribution and the light intensity distribution on the observation plane are further simulated with the changes in the defocus parameter and the phase modulation coefficient. A verification test on the cat-eye laser echo power of the wavefront coded imaging system and that of the conventional imaging system at a 20 m distance are conducted, respectively. Simulations and experiment results show that compared with conventional imaging systems, the wavefront coding imaging system can reduce the retroreflection echo by two orders of magnitude while maintaining better imaging quality through defocusing.

Due to effects of atmosphere and optical subsystem,detector and electronic subsystem in imaging system,there is degradation in imaging process.The degradation of imaging system induces imagery blur.The ability to acquire information from blurred image is debased The technique of image restoration can improve imagery quality,so it can enhance the ability to acquire information from restored image.According to the requirement of image restoration technique,high precision modulate transfer function(MTF) of imaging system is the base of high-quality imagery restored.Since there are differences of MTF between different remote sensors and at different period of same remote sensor,it is important to acquire MTF of imaging system in-flight.The paper presents systematically a in-flight measurement technique of remote sensor MTF,which is called knife edge technique.In the technique,we first analyze its principle and its requirement on targets in images,then introduce in detail several key techniques including sampling method line by line in image,registering line pixels with shifted knife method and fitting method to acquired knife edge.After introducing the technique of image restoration based on imaging system' MTF,the paper shows the improved image on the bases of experiment.The result appears imagery quality is improved obviously.

Medical images are acquired for the purpose of gathering information regarding the disease state of a patient. The quality of the image should be a measure of how a specified task may be performed given the resulting image. Image quality is task dependent; one imaging system may provide images that allow better task performance than another system's for one task, but worse for another task. Determining the quality of an imaging system involves specifying the task of interest, the range of objects that will be imaged, and the observer (human or machine reader) who will perform the task. In radiography it has become common to use Fourier measures to describe image quality through a combination of Fourier‐based measures of system resolution and noise. The Line Spread Function, when Fourier transformed, yields the Modulation Transfer Function (MTF) as a measure of system resolution. Use of the MTF to describe a system's resolution is appropriate when the imaging system is shift‐invariant, that is, the line spread function is independent of position. Image noise is described in the Fourier domain by the Noise Power Spectrum (NPS). We can use the NPS to describe the noise in an imaging system whenever the noise properties are stationary, meaning that the variance and correlations between fluctuations in different locations are not dependent on their absolute location. These Fourier measures of system resolution and noise are commonly combined to give an overall figure of merit known as the Detective Quantum Efficiency (DQE). The DQE describes the signal‐to‐noise transfer characteristics of an imaging system as long as those assumptions of shift‐invariance and noise stationarity are valid. In digital systems the image of an object is affected by the location of the object with respect to the pixel grid. In other words, the detector pixels cause the system to be shift‐variant. In this case the MTF does not describe the resolution properties completely. This is particularly the case for tomographic systems, where the point‐response function is quite position‐dependent. Moreover, in real imaging systems the noise properties will depend on position, most notably because real patients always have structure. So, the Fourier‐domain noise concept of Noise Power Spectrum does not capture all the properties of noise for real imaging systems and tasks. In this talk we will consider a general treatment of the imaging system as a mapping of information from the patient to the data, without the assumptions inherent in Fourier analysis. We will discuss approaches to the characterization of system resolution and noise in terms of position‐dependent parameters. Once such position‐dependent imaging properties of a system are determined, we can use them to calculate measures of image quality that summarize the usefulness of the images for the performance of various visual tasks.

A wavefront coding (WFC) technique provides an extension of the depth of field for a microscopy imaging system with slight loss of image spatial resolution. Through the analysis of the relationship between the incidence angle of light at the phase mask and the system pupil function, a mixing symmetrical cubic phase mask (CPM) applied to 5X-40X micro-objectives is optimized simultaneously based on point-spread function (PSF) invariance and nonzero mean values of the modulation transfer function (MTF) near the spatial cut-off frequency. Optimization results of the CPM show that the depth of field of these micro-objectives is extended 3-10 times respectively while keeping their resolution. Further imaging simulations also prove its ability in enhancing the defocus imaging.

This paper demonstrates a convenient experimental tech- nique for measuring the resolution of a digital imaging system. The spa- tial frequency response of the system is obtained by deriving the modu- lation transfer function (MTF) from the measured contrast transfer function (CTF). Basic signal-processing techniques are used to establish a relationship between the MTF and the CTF. Experimental methodology is discussed with respect to avoidance of shift variation in the CTF. Dis- crete Fourier transformation is applied for a power-spectrum analysis of the MTF. Using the CTF as a measure of performance, a series of ex- periments were carried out to characterize an imaging system based on an integrated CMOS camera. The experimental results showed that this approach can be applied in general, for the assessment of spatial reso- lution for digital imaging systems. © 1998 Society of Photo-Optical Instrumenta- tion Engineers. (S0091-3286(98)00609-6)

엑스선 의료영상이 디지털 시스템으로 발전함에 따라 의료영상의 평가 방법 또한 디지털 시스템에 맞춰 새롭게 개선되었으며 그 중 MTF(Modulation Transfer Function) 측정법은 Fujita이론에 기초한 에지법으로 ISO에 규정되었다. 에지법의 기초인 Fujita이론은 MTF 측정을 위해 슬릿의 각도를 디지털 검출기의 픽셀 열에 대하여 <TEX>$1^{\circ}{\sim}2^{\circ}$</TEX> 기울여 영상을 획득한 후 LSF를 합성하는 것으로 샘플링 간격은 각도에 따라 크게는 1/54배, 작게는 1/28배 감소하게 된다. 본 연구에서 사용된 장비는 Simens사의 MAMMOMAT Inspiration으로 비정질 셀레늄(amorphous selenium) 기반의 <TEX>$0.085{\times}0.085mm^2$</TEX> 의 픽셀 사이즈를 갖는 검출기를 이용하여 presampling MTF를 측정하였다. 측정 방법은 Fujita의 슬릿법와 동일한 방법인 와이어법를 이용하였으며 측정된 영상에서 얻은 픽셀값을 이용하여 엑셀에서 이산 푸리에 변환을 시행하였다. 실험 결과 Fujita이론 대비 약 3배 이상의 샘플링 간격(sampling interval)의 경우 해상도 평가 지수인 10% MTF에서 약 85% 이하의 정확도를 보였으며 선예도 평가 지수인 50% MTF에서 약 93% 이하의 정확도를 나타내었다. 하지만 샘플링 간격이 Fujita 이론 대비 2배 정도 늘어난 경우는 50%와 10% MTF 모두 96% 이상의 정확도를 가진다는 것을 알 수 있었다. Assessments of medical image was improved in accordance with development of medical imaging systems. One of them is edge method to determining MTF(Modulation Transfer Function) based on the Fujita method. Fujita was reduced sampling interval used slightly angulated slit to the direction of pixel array and composited finely sampled LSF to determine presampling MTF. In this study, we investigate the effect of sampling interval on the MTF under a digital imaging system by changing wire angle. The wire method was equivalent to the slit method except signal appearance. A Simens's MAMMOMAT Inspiration with <TEX>$0.085{\times}0.085mm^2$</TEX> pixel size made by amorphous selenium was used and 96% accuracy on MTF in twice sampling interval compared with Fujita was obtained. However, three times of sampling interval showed 93% accuracy on 50% of MTF and 85% accuracy on 10% of MTF.

&lt;p&gt;\n\tWave-front coding, proposed by Dowski and Cathey in 1995, is widely known to be capable of extending the depth of focus (DOF) of incoherent imaging systems. However, benefiting from its very large point spread function (PSF) generated by a suitably designed phase mask that is added to the aperture plane, wave-front coding could also be used to achieve super-resolution without replacing the current sensor with one of smaller pitch size. An image amplification based super-resolution reconstruction procedure has been specifically designed for wave-front coded imaging systems and its effectiveness has been tested by experiment. For instance, for a focal length of 50 mm and f-number 4.5, objects within the range [5 m, infinity] are clearly imaged with the help of wave-front coding, which indicates a DOF extension ratio of approximately 20. The proposed super-resolution reconstruction procedure produces at least 3x resolution improvement, with the quality of the reconstructed super-resolution image approaching the diffraction limit.&lt;/p&gt;

International audience

The line spread function (LSF) is a classical figure of merit used to derive the modulation transfer function (MTF) of an imaging system. However this test cannot be directly applied to cameras based on an infrared focal plane array (IRFPA), as these sampled systems exhibit aliasing effects. ONERA has proposed a new technique called generalized line spread function allowing MTF assessment for sampled imaging systems. A testing of spatial frequency filtering becomes possible until at least twice the Nyquist frequency. The purpose of this paper is to show that this method is well-adapted to IRFPA cameras. In particular, the effects of bad a priori estimation of the characteristics of the camera are discussed. Secondly, we have carried on a laboratory experiment with a widespread infrared imaging system. The purpose is to demonstrate experimentally the advantages of this new method, not only in terms of performances but also in terms of simplicity of implementation and robustness. The infrared imaging system tested is a 512 by 512 Si:Pt IR5120C Mitsubishi camera equipped with a F/1.2 Angenieux lens.

Wavefront coding technology can extend the depth of field of the iris imaging system, but the iris image obtained through the system is coded and blurred and can't be used for the recognition algorithm directly. The paper presents a fuzzy iris image restoration method used in the wavefront coding system. After the restoration, the images can be used for the following processing. Firstly, the wavefront coded imaging system is simulated and the optical parameter is analyzed, through the simulation we can get the system's point spread function (PSF). Secondly, using the blurred iris image and PSF to do a blind restoration to estimate a appropriate PSFe. Finally, based on the return value PSFe of PSF, applying the regularization filter on the blurred image. Experimental results show that the proposed method is simple and has fast processing speed. Compared with the traditional restoration algorithms of Wiener filtering and Lucy-Richardson filtering, the recovery image that got through the regularization filtering is the most similar with the original iris image.

Two main spatial frequency and quantitative calculations and measurements am, used to study the imaging system of three industrial digital radiography (IDR) modules for non-destructive testing (NDT), namely complementary metal oxide semiconductor (CMOS) flat-panel digital detector with 50 mu m pixel pitch, computed radiography (CR) with phosphor imaging plate with 25 mu m pixel pitch and laser-type film digitiser with 50 mu m pixel pitch. The modulation transfer function (MTF) and noise power spectrum (NPS) measurement and calculations were adapted on order to evaluate the image quality of IDR images. The MTF has been used to characterise the resolution properties of analogue and digital X-ray imaging systems and measure image deterioration due to optical factors, such as diffusion of image forming radiation. The NPS is used in determining noise in images produced and the choices of normalisation of the NPS vary slightly from researcher to researcher, but the underlying methodology is consistent. In order to easily compare these two measurements and calculations, the integral of up to the system Nyquist frequency was used as the final image quality quantitative evaluation. For the MTF measurement and calculation, four regions of interest (ROI) were, defined to portray the randomness in performing real testing. The four ROI are then compared with each other. For the NPS measurement and calculation, ten ROI were defined, scattered and averaged to have overall noise estimation. From the measurements and calculations which were done, the averaged MTF at 20% modulation for the laser-type film digitiser system is 6.55 cycles/mm, CR modulated 4.48 and CMOS modulated 2.83 cycles/mm. For NPS measurement and calculation, the result obtained in decreasing order is laser-type film digitiser, CMOS and CR. The laser-type film digitiser system modulates the best transfer function at 20% but does not have the lowest NPS. The lowest and stable NPS is the CR system but it has the lowest modulating capability at 20%. The study shows that in order to perform NDT by using the evaluated modules, the user must know the true capability, of the system and how, it is designed for specific application and discontinuity detection.

Wavefront coding involves the insertion of an asymmetric refractive mask close to the pupil plane of an imaging system so as to encode the image with a specific point spread function that, when combined with decoding of the recorded image, can enable greatly reduced sensitivity to imaging aberrations. The application of wavefront coding has potential in the fields of microscopy, where increased instantaneous depth of field is advantageous and in thermal imaging where it can enable the use of simple, low-cost, light-weight lens systems. It has been previously shown that wavefront coding can alleviate optical aberrations and extend the depth of field of incoherent imaging systems whilst maintaining diffraction-limited resolution. It is particularly useful in controlling thermally induced defocus aberrations in infrared imaging systems. These improvements in performance are subject to a range of constraints including the difficulty in manufacturing an asymmetrical phase mask and significant noise amplification in the digitally restored image. We describe the relation between the optical path difference (OPD) introduced by the phase mask and the magnitude of noise amplification in the restored image. In particular there is a trade between the increased tolerance to optical aberrations and reduced signal-to-noise ratio in the recovered image. We present numerical and experimental studies based of noise amplification with the specific consideration of a simple refractive infrared imaging system operated in an ambient temperature varying from 0°C to +50 C. These results are used to delineate the design and application envelope for which infrared imaging can benefit from wavefront coding.

The optical transfer function (OTF), which correspond to the frequency domain, is of fundamental importance in characterizing imaging ability in optical imaging systems. By using the Collins formula and the optical transfer matrix theory, a simple and unified analytical expression of OTF is presented in any ghost imaging (GI) system. By comparing the spectrum distribution of OTF between different GI systems, one can predict which imaging system can provide better imaging quality when the same imaging object is used. Theoretical and experimental results are also implemented to verify our results.