Optical–digital joint design of refractive telescope using chromatic priors Download: 1151次
Telescope objectives are frequently applied in remote sensing, photography, and security surveillance applications. The performance of refracting telescopes is typically limited by chromatic aberrations that are inherently originated from the long focal length[1]. In order to correct the induced chromatic aberrations, the most common methods are using cemented doublets or triplets that are composed of two or three optical materials with anomalous dispersion, such as
With the maturing of diffractive optical elements (DOE) in design theory and manufacturing, they are more and more frequently used to decrease secondary spectra based on their particular dispersion feature. These designs can have much larger apertures compared to refractive counterparts, yet the good image quality and high transmission can only be achieved in a narrow-band spectrum[7]. Some reflecting telescopes are also subject to chromatic aberrations due to the existence of corrective lenses in the front or rear group, for example, the famous pan-Cassegrain system, where the secondary spectrum can be considerable[8].
We propose a tailored design scheme that utilizes the benefits of a digital imaging processing technique to alleviate the burdensome chromatic aberration correction from optical design. The optical–digital design chain includes firstly an optical design optimization procedure to obtain the optical layout with quasi-monochromatic imaging performance. After that, digital processing is implemented to recover the sharpness of other color channels to fulfill a broad-band design. Results show that a comparable performance can be achieved in a two-lens design with our method when compared with its classic multi-lens counterparts.
In classic Fourier optics, the imaging systems are considered as linear systems, where the point spread function (PSF) distribution is regarded as spatially invariant[9], at least within a local patch of a certain size. Under this assumption, the noise has a devastating influence when recovering the image. We consider the following well-known image formation:
The image formation model is shown in Fig.
The digital correction of optical aberrations therefore becomes solving an inverse problem, expressed as
Recently, one new cross-channel prior proposed by Heide
The mathematical forms of the cross-channel prior in Eqs. (
In the implementation, we use the state-of-the-art blind deconvolution algorithm to resolve the latent images that are not corrected optically[14]. Notice that unlike other work that enforces the cross-channel information sharing as an additional prior term (e.g., Refs. [12,13]), this method includes the cross-channel information transfer in the data fitting term, as represented in Eq. (
In essence, we design the telescope at a specific wavelength (e.g., 550 nm) within a narrow spectrum, which results in a well-corrected image in one color channel (e.g., green). This sharp channel is a reference channel that benefits the information sharing to the other two color channels; hence, the residual chromatic aberrations can be digitally corrected by a post-processing step.
It is worth noting that the reference wavelength is not constrained at one specific wavelength, but any wavelength in the given range. This drastically extends the design space in the optical optimization stage, which also leads to easier correction for other optical aberrations.
We demonstrate this design scheme with a telescope design. The specifications of the proposed telescope are listed in Table
Table 1. Specifications of the Exemplary Telescope
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Figure
Fig. 3. MTF performance at 633 nm of the exemplary design using the joint method before digital processing.
Fig. 4. (a) Spot diagram of the quasi-monochromatic design using the proposed joint method. (b) Spot diagram of the visible spectrum using the conventional design method. The scale difference shows the considerable chromatic aberrations that are unnecessary to correct by using the proposed joint method.
For comparison, we use Wynne’s methods[5] to design the telescope for the same specifications. The final optimized result (shown in Fig.
Fig. 5. Classic design using Wynne’s method[5] to achieve a comparable design under the same specifications in Table 1 .
Notice that the design is to eventually work in the visible spectrum, and therefore, we compare the image performance of our design and the Wynne design in simulation. We simulate the raw images and add Gaussian noise with a variance of 0.005 for both designs in Zemax with the image simulation function, as shown in Figs.
Fig. 7. Performance comparison of the conventional and our designs. (a) Raw image simulated with the proposed design. (b) Image simulated with Wynne’s design. (c) Final corrected image with the proposed method. All of the results are simulated in Zemax with the image simulation function. Our joint design results outperform the conventional Wynne design.
We have run the same tests for different source images, and our method has consistent performance in terms of PSNR. On the other hand, we believe it is more reasonable to test the results with quantitative image quality metrics, e.g., MTF. We use the 12233 chart of International Organization for Standardization (ISO) as a standard input for image quality evaluation. Accordingly, the slanted-edge analysis method is used[15]. The blurred image from the quasi-monochromatic design is shown in Fig.
Fig. 8. Standard ISO 12233 charts of (a) the simulated image and (b) the deconvolved image.
In conclusion, the proposed joint design scheme is validated by applying it to a practical telescope design. The synthetic implementation results exhibit great impact in reducing the complexity of the opto-mechanical structure. We note that this method is not limited to refracting telescope designs, but is also applicable to diffractive and/or catadioptric telescope designs.
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Jingang Zhang, Yunfeng Nie, Qiang Fu, Yifan Peng. Optical–digital joint design of refractive telescope using chromatic priors[J]. Chinese Optics Letters, 2019, 17(5): 052201.