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Abstract
Conventional photon sieves suffer from large chromatic aberration due to diffractive nature and can image only at a single designed wavelength with near zero bandwidth. Here, a novel photon sieve that can image achromatically and simultaneously at multiple wavelengths with wide spectral bandwidth is proposed and demonstrated experimentally. The multispectral achromatic imaging with a single diffractive photon sieve is implemented with harmonic diffraction and wavefront coding, in which harmonic diffraction makes different diffracted orders of multiple harmonic wavelengths on a common focus while wavefront coding through the coded distribution of the pinholes expands the bandwidth of diffracted imaging. Numerical simulations show that when four spectral bands centered at 437.5, 500, 583.3, and 700 nm in the visible range is designed with a cubic wavefront coding parameter α = 30π and a harmonic diffraction order of 5, the bandwidth at the corresponding wavelength band can reach ± 8, ± 9, ± 11 and ± 14 nm respectively, and the total working bandwidth of the harmonic diffraction wavefront coded photon sieve reaches ~84 nm compared with 0.39 nm of the conventional one. Experimental validation was performed using an UV-lithography fabricated wavefront coded photon sieve of a focal length of 500 mm and a diameter of 50 mm at a designed wavelength of 700 nm. The results show excellent agreement with the theoretical predictions.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Diffractive optical elements (DOEs) have become an essential optical element in modern optical systems, such as THz tomography [1], X-ray microscopy [2, 3], and large space telescope [4]. DOEs have many advantages compared to the tradition optical elements, such as light weight, small size, low cost and wide applicable spectral range. Photon sieve is a typical diffractive element, which is evolved from traditional Fresnel zone plate (FZP). FZP is constituted by a series of concentric absorbing and transmitting annular zones while photon sieve uses a great number of pinholes (either non-overlapped or overlapped with random Gaussian distribution) of different sizes to replace the clear zones, which is superior to the counterpart FZP in that higher resolution capability can be achieved. The concept of the photon sieve was first proposed and discussed by Kipp in 2001 [5] and subsequently a detailed theoretical study was carried out by Cao et al in which an analytical formula is provided to calculate the size and position of each pinhole, and also the intensity distribution of the diffracted field in the focal plane [6, 7]. Andersen et al designed and demonstrated an antihole photon sieve with a diameter of 10 cm and a focal length of 1.0 m that works at single designed wavelength of 532 nm with near zero bandwidth [8]. Menon et al proposed a high NA photon sieve that works at 400 nm and applied the photon sieve in a scanning-optical-beam-lithography system [9]. In 2008, Gao et al discussed the imaging characteristics of a photon sieve with a focal length of f = 500 mm and an aperture of 50 mm working at wavelength of 632.8 nm. Compared to a Fresnel zone plate lens with the same feature size, the photon sieve exhibits better imaging performance [10]. In 2010, Chen et al proposed an ultra-large multi-region photon sieve [11] in which the pinhole size in each region was enlarged with different constants relating to maxima positions of the 1st-order Bessel function to facilitate the fabrication and enhance the energy efficiency and the imaging resolution. Sabatyan et al also proposed and demonstrated a photon sieve with overlapped pinholes to further modify and enhance the focusing performance [12, 13]. All the above mentioned photon sieves can work only at a designed single wavelength due to the nature of strong wavelength dependence in DOEs, which greatly limits its applications in optical image. In 2007, Andersen et al proposed a broadband telescope system with a photo sieve as the primary mirror [14]. However, a complex corrective system that contains another DOE and two other mirrors with an even larger aperture must be employed in order to obtain the useful bandwidth of ~40 nm. In 2008, Chung et al [15] fabricated and tested a dual-wavelength photon sieve with a diameter of 3 mm and a focal length of 51.7 mm to operate at two wavelengths of 500 and 600 nm simultaneously. The pinholes for the dual wavelength design were arranged in sectors, concentric with one another, or randomly. In 2009, Zhou et al [16] designed a photon sieve which can work at three discrete wavelengths of 488, 532 and 633 nm. The photon sieve is randomly divided into three regions in which each region is designed for a specific wavelength. However, the three discrete operating wavelengths interfere with each other resulting in large background. In 2015, Zhao et al proposed and demonstrated a broadband imaging using a wavefront coded photon sieve in which a separated cubic phase mask was placed in front of a conventional photon sieve. Results of the experiment show that the working bandwidth of the wavefront coded photon sieve system (WFCPS) reaches ± 14 nm at central wavelength of 632.8 nm, which is ~88 times that of the conventional photon sieves [17]. In 2016, Zhao et al further integrated the wavefront coding into the distribution of pinholes of the photon sieve so that broadband photo sieve imaging can be implemented with a much simplified system [18]. These works demonstrated the possibilities of broadband imaging at a single operating wavelength using DOEs.
In this work, we proposed and showed both theoretically and experimentally that multispectral imaging simultaneously at multiple wavelengths with broad bandwidth is possible by using a single designed diffractive photon sieve for the first time. The novel multispectral photon sieve imaging is implemented with harmonic diffraction and wavefront coding, in which harmonic diffraction makes different diffracted orders of multiple harmonic wavelengths on a common focus while wavefront coding through coded distribution of the pinholes expands bandwidth of diffracted imaging. It is shown that when four spectral bands centered at 437.5, 500, 583.3, and 700 nm in the visible range is designed with a wavefront coding parameter α = 30π, the bandwidth at the corresponding wavelength band can reach ± 8, ± 9, ± 11 and ± 14 nm respectively. A multispectral photon sieve of a focal length of 500 mm and a diameter of 50 mm at design wavelength 700 nm is fabricated with UV-lithography. Experimental imaging was performed both spectrally and totally, and the image results agree with the theory excellently, which breaks the limitation in multispectral imaging using DOEs.
2. Theory
A harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent zone is an integer multiple P of the design wavelength λ0 [19, 20]. The geometry position of mth pinhole at nth ring in a harmonic diffraction photon sieve (HDPS) is described by Eq. (1):
where (xm, ym) is the central location of the mth pinhole, f is the designed focal length of the photon sieve, n is an integer representing the sequential of the rings of the photon sieves, P is an integer representing the optical path-length transition between adjacent zone of a harmonic diffraction lens, λ0 is the design wavelength.When the photon sieve is further wavefront coded, the geometry position of mth pinhole at nth ring in a harmonic diffraction and cubic wavefront coded photon sieve (HDWFCPS) can then be described by Eq. (2):
where k = 2π/λ is the wave number, R is the radius of the photon sieves, α is the wavefront coding parameter, which represents the ability of the optical system to extend the depth of focus. The idea of wavefront coding was first proposed by Dowski and Cathey in 1995 [21] to extend the depth of focus (DOF) of an optical system and to correct axial chromatic aberrations [22]. The major function of the wavefront coding is to modify the point spread function (PSF) of the system in such a way that it becomes invariant over a range of distances around the image plane. The final image with diffraction limit quality is obtained by using digital filtering from the coded images with the modified PSF. When the wavefront coding is employed in the broadband imaging of photon sieves, the PSF of the system becomes invariant over a range of wavelength at the image plane. Broadband imaging of diffractive photon sieves can thus be obtained with digital filtering from the coded images. In Eq. (2), a cubic term, which is the most popularly used in the wavefront coding, is assumed for the purpose of demonstrating multispectral and large bandwidth photon sieve imaging. Other types of the phase coding, such as high-order polynomial phase could also be used in the wavefront coding [23]. Figure 1(a), 1(b) and 1(c) shows a schematic of a conventional photon sieve (CPS), a harmonic diffraction photon sieves (HDPS) and a harmonic diffraction wavefront coded photon sieves (HDWFCPS), respectively (For clarity, only the innermost 30 rings in CPS and 6 rings in HDPS and HDWFCPS are shown). A harmonic diffraction photon sieve differs from a conventional photon sieves in that a phase jump (Φn) at adjacent zone is set to be a multiple (P) of 2π compared with 2π in a conventional one (i.e., P = 1), which means Φn-Φn-1 = 2Pπ. Accordingly, the total ring number of a harmonic diffraction photon sieve is one Pth of that of a conventional photon sieve. Moreover, it is seen from Eq. (1) that if an image is generated by the Pth diffraction order at a designed wavelength λ0, then the diffraction orders of (P ± 1), (P ± 2), (P ± 3) and so on would have a common focus at harmonic wavelength of (Pλ0)/(P ± 1), (Pλ0)/(P ± 2), (Pλ0)/(P ± 3) and so on, respectively. For instance, if diffraction order P = 5, and the design wavelength λ0 = 700 nm are assumed, then the 6th, 7th, and 8th diffraction order at the harmonic wavelengths 583.5, 500, and 437.5 nm respectively, will have a common focus in the visible wavelength range (400 - 700nm), as the structure in Figs. 1(a) and 1(b). Figure 1(c) shows a schematic of a HDWFCPS. On the basis of HDPS (Fig. 1(b)), the pinhole pattern is cubic wavefront coded and the position of the pinhole is modified based on Eq. (2). From Eq. (2) and Fig. 1(c), it can be seen that the coordinates of the pinholes are no longer circularly symmetric, but symmetric about y = x. The sensitivity of diffraction imaging on wavelength is significantly reduced by the introduction of the cubic term in Eq. (2) and the point spread function (PSF) of the HDWFCPS remains unchanged in a much broadened bandwidth. Blurred but consistent images at various designed harmonic wavelengths on a fixed focal plane can be obtained, and diffraction limited images can then be restored by using digital image processing technology. These ideas and theories form the fundamental mechanism of the proposed multispectral and large bandwidth achromatic imaging with a single diffractive photon sieve.
Fig. 1 The schematics of a CPS, HDPS, and HDWFCPS with an aperture of 50 mm, focal length of 500 mm. (a) CPS with design wavelength λ0 = 700 nm; (b) HDPS with P = 5 and λ0 = 700 nm; (c) HDWFCPS with P = 5, λ0 = 700 nm and α = 30π. For clarity, only the innermost 30 rings in CPS and 6 rings in HDPS and HDWFCPS are shown.
3. Simulation
To show the detailed principle and performance of a HDWFCPS, a CPS, HDPS and HDWFCPS with an aperture of 50mm, focal length of 500mm are designed and simulated at design wavelength of 700 nm, respectively. For the CPS, the sizes and positions of each pinhole can be calculated when P = 1 in Eq. (1). The total ring number of the CPS is 892, and the number of pinholes on the outermost zone is 22433 and the minimum pinhole size is 7 µm. For the HDPS and HDWFCPS, the diffraction order P is assumed to be 5, λ0 = 700 nm, and the wavefront coding parameter is α = 30π (a typical wavefront coding parameter as discussed in [18]), the aperture size and the focal length are the same as those of the CPS. It should be mentioned that the parameter P should be selected based on the specific application requirement. Here P = 5 is selected to demonstrate the principle of multispectral imaging of photon sieves in the visible range (400-700 nm) with four wavelength bands. The sizes and positions of each pinhole of the HDPS and HDWFCPS can be calculated with Eq. (1) and Eq. (2) respectively. Because the wavefront coding changes only the position of the pinholes, the size and the number of the pinholes of the HDPS and HDWFCPS are the same, in which the number of pinholes on the outermost zone is 22383 and the minimum pinhole size is 7.01µm. The performance of the CPS, HDPS and HDWFCPS are simulated and compared with MATLAB at harmonic wavelengths 437.5, 500, 583.3 and 700 nm respectively, under the design condition P = 5 and λ0 = 700 nm. The detailed simulation method used in the manuscript for CPS, HDPS and HDWFCPS includes the theoretical calculation of PSFs, MTFs and imaging. The PSFs are calculated based on the total diffracted field distribution of the photon sieve at focal plane which is a summation of all the individual diffracted fields [18] from different pinholes determined by Eq. (1) and Eq. (2). The modulation transfer functions (MTFs) are calculated by taking a Fourier transform of the PSFs, and the simulated images of the photon sieves are obtained by a convolution calculation between a target object (i.e., a patterned test plate) and the PSFs.
Figure 2 shows the simulated PSFs and images at different harmonic incident wavelengths of the CPS and HDPS. It is seen that the PSF of the CPS is clear and diffraction-limited at the design wavelength 700 nm, as expected, but are very diffused at 437.5, 500 and 583.3 nm (Fig. 2(a)). In contrast, the PSFs of the HDPS at all the harmonic wavelengths is clear and diffraction-limited (Fig. 2(b)). The radius of the focal spot at 700 nm is 8.67µm, which is almost same as the diffraction limited radius of 8.44 µm. The radiuses of the focal spot of the rest of three harmonic wavelengths are all close to the respective diffraction limited values. The same phenomena can be seen in the simulated images in Figs. 2(c) and 2(d). The images are obtained by a convolution operation between target and the PSF of the optical system. It is obvious that the images are all diffused (even no details can be identified) at the harmonic wavelengths, but is clear only at the single designed wavelength in the case of CPS, Fig. 2(c), while the images are all clear at the harmonic wavelengths in the case of HDPS, Fig. 2(d).
Fig. 2 Simulated PSFs and images of the CPS and HDPS at different harmonic wavelengths. (a) PSFs of the CPS; (b) PSFs of the HDPS; (c) images of the CPS; and (d) images of the HDPS.
Figure 3(a) shows the modulation transfer function (MTF) curves of the CPS and the HDPS system at the four different harmonic wavelengths. As expected, the MTF curves of the CPS drop rapidly at the three harmonic wavelengths when the incident wavelength deviates from the design wavelength of 700 nm. In contrast, MTF curves of the HDPS show excellent diffraction limited behavior at all the four harmonic wavelengths, which are consistent with those in Fig. 2. The small difference in MTFs among different wavelengths in Fig. 3(a) is due to the inherent nature of the dependence of diffraction on wavelength. Figure 3(b) shows the intensity distribution of the HDPS along the optical axis near focal plane. It is seen that the intensity peaks at the four harmonic wavelengths appear coincidently at 500 mm, which is the designed focal length, as expected.
Fig. 3 (a) MTFs of the CPS and HDPS at harmonic wavelengths; (b) Diffractive intensity distribution of the HDPS near focal plane along optical axis (Z) at different harmonic wavelengths.
As a typical DOE, a CPS has a strong wavelength dependence and suffers from large chromatic aberration. As a result, CPSs can work only at a single designed wavelength with a near zero bandwidth in which working bandwidth can be evaluated by Δλ≈ ± 2λ2f/D2 [24], which is ± 0.196 nm only in our case. A HDPS can realize multi-wavelength operation simultaneously, as proposed and demonstrated in Figs. 2(b) and 2(d), which is a significant progress when compared with a CPS. A major drawback in a HDPS, however, is that the bandwidth at each harmonic wavelength is still near zero (similar to that of a CPS), which still limits its applications. Figure 4 shows the simulated PSFs (Fig. 4(a)) and images (Fig. 4(b)) at different harmonic wavelengths of the HDPS. No surprising, the PSFs and images of the HDPS are diffused when the wavelength deviates from the center of each harmonic wavelengths, i.e., 437.5, 500, 583.3 and 700nm, respectively.
Fig. 4 Simulated PSFs and images of the HDPS at different wavelengths within a certain bandwidth in each harmonic waveband. (a) PSFs of the HDPS; (b) images of the HDPS.
A HDWFCPS can achieve multispectral and large bandwidth operation simultaneously when a cubic wavefront coding is introduced into the distribution of the pinholes of the HDPS, as described by Eq. (2) and Fig. 1(c). Figure 5 shows the performance of a designed HDWFCPS over a bandwidth at each harmonic wavelength with a wavefront coding parameter α = 30π while all other parameters remain the same as those used in the HDPS. The centers of each harmonic wavelength of the HDWFCPS are the same as those in the HDPS, i.e., 437.5, 500, 583.3 and 700 nm, respectively.
Fig. 5 The simulated imaging behaviors of a HDWFCPS at different harmonic wavelength bands with a coding parameter α = 30π. (1a, 2a, 3a, 4a): PSFs; (1b, 2b, 3b, 4b): intermediate blurred images; (1c, 2c, 3c, 4c): restored clear images.
In Fig. 5, Figs. 5(1a)-5(4a) show the PSFs of the HDWFCPS with a coding parameter α = 30π at different harmonic wavelength bands from 429.5 to 445.5 nm (centered at 437.5 nm with a bandwidth of 16 nm), 491 to 509 nm (centered at 500 nm with a bandwidth of 18 nm), 572.3 to 594.3 nm (centered at 583.3 nm with a bandwidth of 22 nm) and 686 to 714 nm (centered at 700 nm with a bandwidth of 28 nm), respectively. It is seen that the PSFs within the bandwidth of each harmonic wavelength remain almost unchanged, which means that the PSFs of the HDWFCPS is independent of the wavelength within the bandwidth. This bandwidth can be considered as effective working bandwidth of the HDWFCPS. Figures 5(1b)-5(4b) show the blurred intermediate images (i.e., before digital filtering) within the effective bandwidth of each harmonic wavelength. The blurred intermediate images in Figs. 5(1b)-5(4b) are obtained by a convolution calculation between a target object (i.e., a patterned test plate) and the PSFs shown in Figs. 5(1a)-5(4a), respectively. The images are almost identical at different wavelengths within each bandwidth although it is blurred, which means that images are wavelength independent and can be restored by one filtering function. Figures 5(1c)-5(4c) show the restored images of the HDWFCPS within each harmonic wavelength band, respectively. The image restoration is performed by a deconvolution operation (Wiener filtering) between the blurred intermediate images shown in Figs. 5(1b)-5(4b) and an averaged PSF (i.e., filtering function) shown in Figs. 5(1a)-5(4a) within the effective bandwidth. It is seen that all the intermediate blurred images can be well restored by using a fixed filtering function and the resolution of all restored images is almost the same as that of the CPS and the HDPS at the designed wavelengths.
The effective bandwidth of the HDWFCPS at each harmonic wavelength can be evaluated by the consistency of the MTF function in the vicinity of each harmonic wavelength. Figure 6 shows the MTFs of the HDWFCPS around each harmonic wavelength. It is seen that the MTFs remains unchanged within a certain range of the harmonic wavelength. When the working wavelength deviates significantly from the harmonic wavelength, the MTFs also deviate significantly from the consistency. The wavelength ranges of the MTFs deviating from the consistency can be defined as the effective bandwidth, from which the bandwidths can be determined as 16 nm, 18 nm, 22 nm, and 28 nm, respectively, at the harmonic wavelength 437.5 nm, 500 nm, 583.3 nm, and 700 nm, if the bandwidth is defined as wavelength separation between the center of each waveband and the wavelength at which the MTF curve drops at normalized spatial frequency of 0.6, as shown in Fig. 6. This definition of the bandwidth can also be backed up in Fig. 5 in that the image quality at the boundary wavelengths of each waveband begins to show decreasing. As a comparison, the MTFs of HDPS shown in Fig. 6 exhibit a different behavior from that of the HDWFCPS. The MTF in HDPS is high (diffraction limited) at each harmonic wavelength, but drops quickly when the wavelength deviates from the harmonic wavelength, which is also witnessed in Fig. 4.
4. Experiments
The proposed multispectral and broadband imaging with a single HDWFCPS is demonstrated and compared with a CPS (design wavelength 700 nm) and a HDPS with the same focal length (500mm), aperture size (50 mm) and four wavebands in the visible range as mentioned above. The wavefront coding parameter of the HDWFCPS is set as α = 30π. The CPS, HDPS, and HDWFCPS are fabricated on metallic Chromium(Cr) thin film on glass substrate using UV lithography. Experimental imaging setup is shown in Fig. 7(a). The inset of Fig. 7 shows the photo and magnified image of the central region of the fabricated HDWFCPS. The light source is a tungsten halogen lamp (THORLABS SLS301), which emits light covering the visible range as required. A common convex lens is used to focus the visible light onto the resolution target. The resolution target used in the experiment is USAF1951. A bandpass filter is placed between the common convex lens and the resolution target, in which different bandpass filters can be switched for different waveband imaging. The transmission curves of different bandpass filters for the designed 4 wavebands are shown in Fig. 7(b). The bandwidth of full width at half maximum (FWHM) of the four filters (commercially available from Thorlab) is the same, ~10 nm (THORLABS, FB440-10, FB500-10, FB580-10, FB690-10). A collimator with a focal length 550 mm and a diameter of 55 mm are used to collimate the optical path. A CCD with pixel size 4.54 μm (AVT Prosilica GX2750C) is placed at the focal length behind the photon sieve. The imaging information from the CCD is driven and processed by a computer.
Fig. 7 (a) Experimental setup of a HDWFCPS imaging system; (b) Transmissions of four bandpass filters with a FWHM bandwidth of 10 nm and centered at wavelength 440 nm, 500 nm, 580nm, and 690 nm, respectively.
The performance of the CPS and the HDPS are evaluated and compared firstly. Figure 8 shows the images of the CPS and the HDPS at those designed four wavebands. It is seen that, as a DOE, the CPS, Fig. 8(a), can only show a blurred image around the wavelength 690 nm with a bandwidth of 10 nm, no images (even blurred images) can be seen in the other three wavebands because the working wavelengths are too far away from the design wavelength 700 nm. As a comparison, the HDPS can image at the designed four wavebands at exactly the same focal length, Fig. 8(b), although it suffers from large chromatic aberration at all the four wavebands because, in principle, a HDPS can work only at exactly the designed harmonic wavelengths with near zero bandwidth. It is also noticed that the images of the HDPS at the four wavebands exhibit the similar chromatic aberration to that of the CPS because the bandwidth of the wavelength filters used in the four wavebands is the same, i.e., 10 nm.
Fig. 8 The blurred images of the CPS and HDPS at four designed harmonic wavebands with a bandwidth of 10 nm. (a) CPS; and (b) HDPS.
Figure 9 shows the experimental imaging results of the HDWFCPS with a wavefront coding parameter α = 30π. Figure 9(a) is the experimentally measured PSFs of the system, which is similar to that in the simulation, Fig. 5, i.e., it takes triangle shape and keeps almost unchanged at the four wavebands with a bandwidth of 10 nm each. Figure 9(b) is the intermediate blurred images, which is directly taken by the CCD experimentally, of the HDWFCPS at the four wavebands, in which all the intermediate blurred images are almost identical so that these blurred images can be restored with an unified digital filter. The restored images are shown in Fig. 9(c). The image restoration is implemented with Wiener filtering technique in which the blurred intermediate images shown in Fig. 9(b) are de-convoluted with the filtering function of the PSF shown in Fig. 9(a). It is seen that all the intermediate blurred images at the four wavebands can be well restored. It should be emphasized that the blurred images shown in Fig. 8(b) in HDPS cannot be restored by the same filtering method as that used in Fig. 9 in HDWFCPS. The fundamental physical mechanism is that when wavelengths deviate from the center wavelength in each waveband in HDPS, the MTFs at those deviated wavelengths drop rapidly and zeros appear in the MTFs (as shown in Fig. 6), resulting in the loss of spatial frequencies in both filtering functions and the images in HDPS, and consequently, no images can be restored in HDPS.
Fig. 9 (a) Measured PSF of the HDWFCPS with a coding parameter α = 30π; (b) Intermediate blurred image produced by the HDWFCPS; (c) Restored image of the HDWFCPS.
To evaluate the performance of the imaging of the HDWFCPS, Figs. 10(a) and 10(b) show the MTFs of the HDWFCPS before and after the image restoration, i.e., Figs. 9(b) and 9(c). It is seen that the MTFs in Fig. 10(a) in different wavebands are almost identical and no zeros appear in the MTF curves from low to high frequency, which means that no information of spatial frequencies in the images after wavefront coding will be lost although the MTFs is lower than the diffraction limit. Figure 10(b) is the corresponding MTFs of HDWFCPS at the four wavebands after restoration and its comparison with that of a CPS designed at 632.8 nm. All the MTFs agree very well each other, and very close to that of the CPS designed and fabricated at 632.8 nm wavelength (He-Ne laser can be used for experiment).
Fig. 10 (a) MTFs of HDWFCPS at the four wavebands before restoration; (b) MTFs of HDWFCPS at the four wavebands after restoration.
Finally, the imaging performance of the HDWFCPS working under the mixture the four wavebands centered at 440 nm, 500 nm, 580 nm, and 690 nm with total bandwidth experimentally of 40 nm. The mixture of the banded visible light is obtained by placing a filter disc that contains 4 wavebands filters as used above behind the tungsten halogen lamp light source (as shown in Fig. 11(a)). Then a convex lens was used to focus the four-waveband mixed light onto a double frosted glass to scatter and diffuse the light uniformly. The other part of the image system is the same as that in Fig. 7(a). The intermediate blurred image under the illumination of four-waveband mixed light is shown in Fig. 11(b), and the corresponding restored image is shown in Fig. 11(c). The image restoration is implemented with the same method as that used in Fig. 9, in which the blurred intermediate image shown in Fig. 11(b) is de-convoluted with the filtering function which is an averaged PSF in the four wavebands shown in Fig. 9(a). It is seen that the image can be well restored and the optical resolution is estimated to be ~45 lp/mm, close to the optical resolution of CPS designed at 632.8 nm of ~50.8 lp/mm. The slight loss of optical resolution in the HDWFCPS may be attributed to coding and decoding processes in the wavefront coded imaging in that additional optical and electronic noises are introduced into the images.
Fig. 11 Images of the HDWFCPS under the illumination of four-waveband mixed light source. (a) Experimental arrangement; (b) Intermediate blurred image; (c) Restored image.
5. Conclusions
In this paper, a multispectral and large bandwidth achromatic imaging with a single diffractive photon sieve was proposed and experimentally demonstrated for the first time. DOEs usually suffer from large chromatic aberration so that it can work only at single wavelength with near zero bandwidth. The proposed and demonstrated multispectral HDWFCPS imaging with large bandwidth represents a new type of photon sieves that combines the harmonic diffraction and wavefront coding, which breaks the limitations of conventional DOEs in that HDWFCPS can work not only at multiple wavelengths simultaneously but also with wide bandwidth simultaneously. In addition, depth of focus of the HDWFCPS system can also be increased. Experimental validation was performed using an UV-lithographically fabricated HDWFCPS of a focal length of 500 mm and a diameter of 50 mm at designed wavelength 700nm with 4 working wavebands in the visible range. The results show excellent agreement with the theoretical predictions. The demonstrated HDWFCPS provides a novel idea on the multispectral and wide bandwidth imaging operation of using diffractive optical elements, which has great potentials in applications of large space telescope, remote sensing, and biomedical imaging.
Funding
National Natural Science Foundation of China (NSFC) (61775154); The Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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