Abstract
Imaging through scattering media is vital for biomedical and astronomical applications. While memory-effect-based methods, including speckle correlation and speckle deconvolution, are characterized by their simplicity and convenience, strong background illumination often degrades reconstruction. We propose a symmetrized speckle method based on the frequency-domain characteristics of symmetrical speckle patterns via flipping and stitching speckles. Experimental validations were conducted on both transmissive and reflective objects under background illumination from various directions. For a white light illumination scene, we additionally propose and demonstrate a blind-deconvolution modified symmetrized speckles method to solve the chromatic dispersion problem. Compared to existing techniques, our approach achieves superior reconstruction quality under diverse illumination, demonstrating unique advantages for scattering imaging.
© 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fog, white paint, and biological tissue are common in real life, and light scatters when it passes through these materials. Therefore, imaging objects hidden behind scattering media is a tough challenge. Due to the scattering effect of the scattering medium on the incident light, the outgoing light field becomes chaotic and random, and a scattering pattern can only be obtained on the image plane [1,2]. Currently, there are numerous methods in realizing imaging through scattering media, such as optical coherence tomography [3], wavefront-shaping technique [4–7], phase conjugation technique [8–11], adaptive optics technique [12,13], and polarization speckle analysis technique [14,15]. Compared with these methods, the scattering correlation and scattering deconvolution methods [16] based on the memory effect [17,18] have the advantages of being able to take a single shot, fast computation, recovering the image quality independent of the object complexity, and being able to retain the object position information.
For the memory effect-based methods, in practice, the experimental system needs to be calibrated to ensure that the speckle image detected on the camera plane is uniform and symmetric. However, in the real scenarios, the presence of background light often causes asymmetry in the speckle image, leading to a steep reduction in imaging capability of imaging methods based on the memory effect. To address this issue, researchers have proposed the singular value decomposition (SVD) technique [19], self-calibrated homomorphic filtering (SCHF) method [20] the Zernike-based background fitting method [21]. However, the SVD method requires multiple attempts to determine the number of principal components, the SCHF method requires a repetitive iterative calibration process, and the Zernike-based background fitting method necessitates a complex fitting process.
Here, we introduce a method that greatly improves the effect of illumination on the reconstruction results by simply symmetrizing and filtering the speckle image. Our method utilizes the principle that the phase spectrum of symmetric speckle is constant to 0 after Fourier transform to the frequency domain, and for the speckle image obtained in the presence of background light, we do horizontal flip, vertical flip, and horizontal-vertical flip, the three flipped images are then stitched together with the original image to eliminate the effect of phase factor, and then do the filtering process after that. On this theoretical basis, experiments under different types and bandwidths of illumination are designed for demonstration. The final results show that the proposed method contributes to reliable image reconstruction and maintains its effectiveness in the challenges posed by strong background light as well as broadband illumination. Therefore, the innovations of this paper can be summarized as follows: the speckle symmetrized method offers the advantage of faster and simpler computation compared to other approaches; it has been experimentally validated to be effective for different objects with varying luminescence characteristics under diverse imaging conditions; and by combining it with blind deconvolution, the issue of signal broadening under broadband illumination is resolved. Overall, the speckle symmetry method has great potential for practical scattering imaging applications.
2. Principle
The imaging method through scattering media based on the memory effect necessitates that the size of objects suitable for this technique falls within the memory effect's range. The range of the memory effect is generally quite limited, in which case objects can be approximated as point sources. At this point, the light received on the camera plane can be approximated as a Gaussian distribution. However, when the background illumination is intense or the scattering medium exhibits a high degree of anisotropy, the speckle distribution captured by the camera may deviate from a Gaussian form and assume other configurations. Here, we use the Gaussian distribution as an example; the general case for light distribution is provided in the Supplement 1.
A speckle image conforming to perfectly symmetric Gaussian illumination can be represented as follows:
When strong background illumination is present in the imaging environment, the background light typically strikes the scene from the side or rear. In such cases, the illumination on the imaging plane may be regarded as an asymmetrical Gaussian distribution, wherein the center of the Gaussian light distribution has undergone translation in both the x and y directions. When the center of Gaussian light is shifted horizontally and vertically:
At this point, the scattering image becomes:
the transformation to the Fourier domain yields:It can be noticed that compared to symmetric illumination, the Gaussian center shift introduces a phase factor exp(-j2π(ux0 + vy0)), resulting in a redistribution of the frequency domain energy in the horizontal and vertical directions, creating the horizontal and vertical bright lines shown in Fig. 1 (b) which will significantly compromise the imaging quality of subsequent material reconstruction. This is due to the characteristic of the Fourier transform: displacement in the spatial domain corresponds to phase shift in the frequency domain. Spectrum is the basis of speckle image processing based on memory effects, and is used to achieve high-pass filtering of speckle images, which can yield an image with uniform illumination. However, the phase factor in the spectrum causes low-frequency information to be unable to be completely filtered out when filtering the speckle pattern, resulting in the presence of stripes (Fig. 1 (c)), which in turn causes the final speckle correlation or convolution imaging effect to be greatly reduced or even unable to image.
Fig. 1. (a) Speckle image detected when the center of Gaussian illumination is shifted horizontally and vertically. (b) Fourier transform results for (a). (c) High-pass filtering results for (a). (d) Flipped and stitched image of this speckle image. (e) Fourier transform results for (d). (f) High-pass filtering results for (a) based on the symmetrized speckle in (d).
To avoid this problem, we perform horizontal flipping, vertical flipping, and combined horizontal-vertical flipping on the image. The three transformed versions are then stitched with the original image as shown in Fig. 1 (d). The flipped and stitched image is:
In contrast to Eq. ( 5 ), the directional phase factor exp(-j2π(ux0 + vy0)) is superimposed on exp(±j2π(ux0 ± vy0)) after the flip to form the real term cos(2πux0)cos(2πvy0), which eliminates the directionality of the imaginary part. And because the cosine function is an even function, resulting in a symmetrical distribution of the frequency domain energy in the horizontal and vertical directions, the bright lines in Fig. 1 (b) are canceled out. As shown in Fig. 1 (e), at this point the low-frequency components are concentrated at the center, allowing the subsequent high-pass filter with a radius of 25 pixels to completely filter them out. Figure 1 (f) shows the new filtered image, and the contrast of the speckle is significantly improved.
We know that the two-dimensional Fourier transform of a real-valued even function is also a real-valued even function with a constant phase spectrum of 0 and only an amplitude spectrum. For a centrosymmetric scattering image under Gaussian illumination, the intensity variation across all directions conforms to an even function distribution. However, when the Gaussian illumination center shifts, the directional intensity variations deviate from this even function profile. To address this anomaly, we flip and stitch the image to restore the even-function-compliant intensity distribution. Subsequent application of the Fourier transform to the composite image effectively removes the effects of asymmetric illumination. Similar to conventional speckle preprocessing approaches, our approach involves no pixel compression throughout the entire processing chain, thereby avoiding the introduction of blurring that could degrade performance.
When imaging through a scattering medium, the speckle image I detected by the camera is the convolution of the object intensity distribution O and point spread function (PSF) of the system [23]:
By performing autocorrelation on the speckle image I detected by the camera, we can obtain:
Therefore, for the speckle obtained after the above-mentioned filtering operation, the object image can be obtained by using the deconvolution method when the PSF is known. Based on the characteristic that the autocorrelation of the PSF is a Dirac function, the object image can be obtained by performing a phase retrieval algorithm on the speckle autocorrelation result.
3. Experiments under strong background illumination
To validate the effectiveness of our method in imaging through a scattering medium under strong background illumination, we set up three experimental systems, as shown in Fig. 2 .
Fig. 2. (a) Experimental setup for imaging a transmissive object hidden behind a scattering medium under strong background illumination. (b) Experimental setup for imaging of a dark object hidden behind a scattering medium under strong background illumination. (c) Experimental setup for imaging of a reflective object hidden behind a scattering medium under strong background illumination.
Figure 2 (a) shows the experimental system of imaging through scattering medium under strong background illumination from an additional light source. An incoherent light source (single-color LED, 625 nm nominal wavelength, 17 nm bandwidth, 920 mW, Thorlabs) is illuminated on an object, which is element “4” of the first group of the U.S. Air Force resolution target, and the light from the object is transmitted through a scattering medium (UV Fused Silica Ground Glass Diffuser, 220 Grit, Thorlabs) and received by a camera (monochrome camera, 5488 × 3672 pixels, 2.4 mm pixel size, Huateng Vision). To construct a scattering imaging environment under strong background illumination, another incoherent light source (GCI-060401, 620 nm wavelength, Daheng Optics) is placed on one side of the optical path so that its outgoing light irradiation can be received by the camera after passing through the scattering medium. Then, the camera detects the scattered light from the object as well as the background light, as shown in Fig. 3 (a). The object distance in this imaging system is 60 cm, and the image distance is 7 cm. The distance between the background light source and the scattering medium is equal to the distance between the object and the scattering medium.
Fig. 3. (a)-(c) Speckle images detected from the experimental systems in Figs. 2 (a)– 2 (c). (d)-(f) Speckle images by high-pass filtering of the symmetrized speckles from (a)-(c).
Figure 2 (b) shows the experimental system of imaging dark object through scattering media under strong background illumination. The light source, scattering medium, camera, object distance and image distance are the same as in Fig. 2 (a). An incoherent light source is illuminated on an opaque object “4”, which is the same size as the object in Fig. 2 (a) but is opaque, with its surroundings being transparent. The light projected around the object passes through a scattering medium and is captured by the camera. Then, the camera detects the scattered light from the background illumination is shown in Fig. 3 (b). It can be seen that the contrast of the speckle in this imaging environment is extremely low.
Figure 2 (c) shows the experimental system of imaging through scattering medium under strong background illumination from a light source directly behind. An incoherent light source is illuminated on an object “4”, which is the same size as the object in Fig. 2 (a) and is opaque on one side and reflective on the other. The light reflected from the object is transmitted through a scattering medium and received by a camera. To construct a scattering imaging environment under strong background illumination, another incoherent light source is placed behind the object so that its outgoing light irradiation around the object can be received by the camera after passing through the scattering medium. Then, the camera detects the scattered light from the object as well as the background light, as shown in Fig. 3 (c). The light source, scattering medium, camera, object distance and image distance are the same as in Fig. 2 (a).
Fig. 4. Comparison of the results of each reconstruction method. (a) The hidden objects in corresponding experiments shown in Fig. 2 . (b) Autocorrelation phase retrieval results of the SVD method [19]. (c) Deconvolution results of the SVD method [19]. (d) Autocorrelation phase retrieval results of the SCHF method [20]. (e) Deconvolution results of the SCHF method [20]. (f) Autocorrelation phase retrieval results of our symmetrized speckles method. (g) Deconvolution results of our symmetrized speckles method.
Fig. 5. (a) Object “3” hidden behind the scattering medium. (b) Speckle pattern of object “3” under strong background illumination. (c) Autocorrelation phase retrieval results of our symmetrized speckles method. (d) Deconvolution results of our symmetrized speckles method. (e) Object “0” hidden behind the scattering medium. (f) Speckle pattern of object “0” under strong background illumination. (g) Autocorrelation phase retrieval results of our symmetrized speckles method. (h) Deconvolution results of our symmetrized speckles method.
For the above three sets of experiments, the detected speckle images are processed with symmetry and then filtering, and the results are shown in Fig. 3 (d) to (f). It can be seen that while the light has been homogenized, the speckles contrast has been significantly improved. For the speckle images in Fig. 3 (a)-(c), reconstructions via autocorrelation phase retrieval and speckle deconvolution were performed using SVD, SCHF, and our proposed symmetrized speckle method. Quantitative comparison of the reconstruction fidelity, measured by SSIM, is presented in Fig. 4 . To avoid the influence of background noise on the results, only the SSIM of the object part is calculated. As shown in the column (b) of Fig. 4 , it can be seen that SVD almost fails in performing the autocorrelation phase retrieval algorithm when the strong background illumination is present, and the object cannot be reconstructed. The results obtained using SVD in the deconvolution method are shown in Fig. 4 (c), where the object can be reconstructed well when there is a strong background illumination from one side (Fig. 4 (c1)), but the deconvolution reconstruction results are not good when the strong background illumination is located behind the object (Fig. 4 (c2) and (c3)). When we apply the SCHF method, as shown in Fig. 4 (d) and (e), the autocorrelation phase retrieval algorithm fails completely, and the quality of the reconstruction results by the deconvolution method is relatively poor, especially when the strong background illumination is incident on the dark object from directly behind. For the experimental optical setup in Fig. 2 (b), the sparsity condition [23] was not satisfied and the speckle contrast corresponding to the dark object was very low, resulting in extremely poor autocorrelation results and failure of the phase retrieval algorithm; however, when it comes to deconvolution method, our approach still outperforms the other two, as shown in Fig. 4 (g2). For the optical paths in Fig. 2 (a) and (c), our method shows significantly better reconstruction results than the other two methods in both autocorrelation phase retrieval algorithm and deconvolution method, as shown in Fig. 4 (f1), (f3), (g1) and (g3). Compared with SVD, the symmetrized speckles method does not require repeated trials to determine the number of principal components, nor does it require adaptive or fitting processes like SCHF and Zernik fitting methods. Therefore, our method is simpler and more convenient than these methods.
To further demonstrate the applicability of our method, we examine objects with structural symmetry: “0” and “3”. These objects correspond to the “0” on the U.S. Air Force resolution target and the “3” in the first group. The experimental system is identical to that shown in Fig. 2 (a). From Eq. ( 3 ) to ( 7 ), it can be seen that this method imposes no symmetry requirements on the object. The reconstruction results shown in Fig. 5 show that the performance of this method remains unaffected for objects with structural symmetry.
4. Experiment under white light illumination
Monochromatic light sources are used in all of the above experiments, but most of the illumination in the actual scene is white light. The previous method is not applicable to broadband illumination situations. At present, when the scattering medium is irradiated by broadband light, not only spatial speckle but also spectral speckle is generated, resulting in the time broadening of the pulse formed from the autocorrelation of the PSF [24], this leads to poor imaging results or even the inability to image. Therefore, white light imaging research is also very meaningful. Current methods for imaging through scattering media under broadband illumination include blind deconvolution method [25,26] and single-shot OTF-based reconstruction method [27]. Figure 6 compares results from both approaches, showing that single-shot OTF-based reconstruction method yields superior outcomes and this method features more relaxed constraints.
Fig. 6. (a) Object “3” hidden behind the scattering medium. (b) Autocorrelation of object’s speckle under white light illumination. (c) Reconstruction results from the blind deconvolution method. (d) Reconstruction results from the single-shot OTF-based reconstruction method.
To further verify the effectiveness of our proposed speckle symmetry method, the experiment of imaging through a scattering medium under white light illumination is implemented. We use the experimental setup diagram shown in Fig. 2 (a) and change all the light sources to white light (GCI-060411, 440-670 nm wavelength, Daheng Optics). At this point the speckle captured by the camera is shown in Fig. 7 (a), and its autocorrelation is shown in Fig. 7 (b): the autocorrelation of the object is completely drowned out by background noise, resulting in phase recovery failure (Fig. 7 (c)). Moreover, due to the presence of background light, the single-shot OTF-based reconstruction method also failed (Fig. 7 (d)).
Fig. 7. Experimental results of imaging through scattering layers under white light illumination and white light background illumination. (a) Speckle image. (b) Autocorrelation of (a). (c) Reconstruction of (b) through phase-retrieval algorithm. (d) (a) after processing by the single-shot OTF-based reconstruction method. (e) Speckle image after high-pass filtering and symmetrizing the speckle in (a). (f) Autocorrelation results of (e). (g) Reconstruction from (f) through phase-retrieval algorithm. (h) Results of blind deconvolution performed on (f). (i) Reconstruction from (h) through phase-retrieval algorithm.
To eliminate the influence of strong background illumination, we used the symmetrized speckle method, as shown in Fig. 7 (e). But from Eq. ( 8 ) and Eq. ( 9 ), we know that when white light illumination is present, there is cross-correlation between PSFs of adjacent wavelengths, causing the PSF autocorrelation to expand from a Dirac function distribution to a near-Gaussian distribution. Thus, when applying the phase retrieval algorithm to the autocorrelation of the object speckles the reconstruction fails, as evidenced in Fig. 7 (g). This failure occurs because the object's autocorrelation convolves not with a Dirac function, but with a function approximating a Gaussian distribution [25–31] (Fig. 7 (f)). For the broadened PSF and the autocorrelation of object speckles, unlike in the case of narrow-bandwidth illumination, we use the blind deconvolution method [25,26] to iteratively estimate and constrain the autocorrelation results under broad-bandwidth illumination. The standard deviation of the Gaussian distribution was estimated via power spectrum analysis, and the size of the Gaussian blur kernel was calculated. Based on this, a reasonable convergence radius was established. Ultimately, we use a Gaussian kernel to fit the blurred autocorrelation image, obtaining a 21 × 21 Gaussian blur kernel with a convergence radius of 3.1. Then, we use the Richardson-Lucy algorithm to perform 25 iterations to obtain the blind deconvolution result (as shown in Fig. 7 (h)), thereby mitigating spectral broadening effects. Subsequently, phase retrieval operations are performed on the processed results to reconstruct the object, the reconstructed object is presented in Fig. 7 (i). It can be noted that the use of a Gaussian kernel for blind deconvolution is an effective engineering approximation. Within the memory effect range, the speckle patterns from different spectral components are correlated to some degree, and their ensemble average causes the autocorrelation of the broadband PSF to often assume a smooth, peaked profile, which can be reasonably fitted by a Gaussian function [25]. However, this model has inherent limitations. Since the memory effect range is wavelength-dependent, the true broadband speckle autocorrelation may deviate from a perfect Gaussian form, which contributes to the residual artifacts observed after deconvolution. Compared to the single-shot OTF-based reconstruction method, our approach exhibits weaker performance under dark-field conditions. However, when subjected to intense background illumination, the single-shot OTF-based reconstruction method becomes entirely ineffective, whereas our method successfully restores the object. By calculating the SSIM of the reconstructed result, we can see that our method demonstrates satisfactory performance under white light illumination.
To further verify the applicability of the symmetrized speckles method, we replaced the light source used as background illumination in the optical path with incandescent lamp which is commonly used for general lighting in laboratories, and the scattering medium was a three-layer parafilm, as shown in Fig. 8 (a). The low-contrast speckles obtained in this scenario are shown in Fig. 8 (b), where the autocorrelation results exhibit broadening (Fig. 8 (c)), and the failed phase-retrieval result is shown in Fig. 8 (d). By applying the symmetrized speckles method, we obtained speckles with higher contrast (Fig. 8 (e)), and using blind deconvolution, we achieved better autocorrelation results (Fig. 8 (f)). The phase recovery algorithm yielded the results shown in Fig. 8 (g). By calculating the SSIM of the reconstructed result, we can see that our method is still effective in bright scenes.
Fig. 8. (a)Experimental results of imaging through scattering layers under white light illumination and fluorescent lights’ background illumination. (b) Speckle image. (c) Autocorrelation of (a). (d) Reconstruction of (c) through phase-retrieval algorithm. (e) Speckle image after high-pass filtering and symmetrizing the speckle in (b). (f) The result of blind deconvolution after autocorrelation on (e). (g) Reconstruction from (f) through phase-retrieval algorithm.
5. Conclusion
In summary, we propose and demonstrate an imaging method through a scattering medium under strong background illumination. By implementing speckle symmetrization followed by adaptive filtering operations, the proposed technique successfully reconstructs high-fidelity images of objects obscured by scattering media and contaminated by extraneous light sources, demonstrating consistent performance across both monochromatic and broadband illumination scenarios. Notably, the algorithm achieves this through computationally simple image flipping and stitching operations, eliminating the need for complex iterative optimization or surface fitting procedures. This method holds significant potential for application in imaging through scattering media. Moreover, it remains applicable in non-line-of-sight imaging, which constitutes one of our subsequent research directions. However, our approach still exhibits certain limitations. For instance, the speckle correlation method becomes ineffective when the images captured by the camera fail to satisfy the sparsity feature. Furthermore, reconstruction results under white light illumination continue to suffer from artefacts. We well subsequently consider employing adaptive methods to refine the fitting process and thereby enhance the final reconstruction results. Consequently, the applicability of the speckle symmetrized method requires further expansion, which will enable its potential application in biomedical diagnostics and optical sensing systems.
Funding
National Natural Science Foundation of China (62105146, 12274224, 12504349); Natural Science Foundation of Jiangsu Province (BK20210290); Key Laboratory of Aerospace Information Materials and Physics (NUAA) Foundation (XCA24050-06); Fundamental Research Funds for Central Universities (NS2025035).
Disclosures
The authors have no conflicts of interest to declare.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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