Due to the optical anisotropy of liquid crystal materials, a polarizer is typically required in front of the liquid crystal lens when used in imaging systems. However, the polarizer reduces the intensity of incident light and increases the size of the imaging system. This has made polarization-free imaging a key research area for liquid crystal lenses. Currently, there are three main methods for achieving polarization-free imaging. The first method utilizes the Kerr effect in blue-phase liquid crystals to control the refractive index in different regions. This method eliminates the need for alignment layers, significantly simplifying the lens manufacturing process. However, blue-phase liquid crystals require high driving voltages and have a narrow temperature range, limiting their practical applications. The second method is the “full lens” approach, which stacks two liquid crystal lenses with orthogonal optical axes. Although this combination can modulate natural light, it increases the thickness and cost of the device. The third method employs a polarization-free imaging algorithm (PFI). Previous approaches have achieved polarization-free imaging by subtracting the image in the lens’s non-working state from the image in the working state, thus removing the unmodulated polarized light. However, this method requires capturing two images, resulting in relatively long processing times. Therefore, a faster, device-independent method is needed for polarization-free imaging with liquid crystal lenses. The deconvolutional polarization-free imaging (DPFI) method proposed in this paper requires only a single image to eliminate the effects of unmodulated polarized light, significantly improving processing speed. Initially, the point spread function (PSF) images of the liquid crystal lens without a polarizer are captured and stored in the DPFI algorithm program. The algorithm then restores the image by applying the corresponding PSF when the liquid crystal lens is in operation.

The traditional PFI algorithm works as follows: first, we capture an image with the e-light focused and the o-light defocused while the liquid crystal lens is in the on state. Next, we capture another image with both the e-light and o-light defocused while the lens is in the off state. Finally, we subtract half of the grayscale value of the latter image from the former image, which removes the o-light component and results in an image where only the e-light is focused. In the DPFI method, we first experimentally capture the PSF by recording the diffused light spot of a point light source through the liquid crystal lens imaging system. Then, we capture the imaging result of the object at the corresponding point light source position. The imaging result can be described as the convolution of the object image with the imaging system’s PSF. In the frequency domain, the convolution process is represented as a product, and the deconvolution process involves dividing the imaging result in the frequency domain by the PSF in the frequency domain (optical transfer function, OTF). This yields the object’s frequency domain representation, which is then transformed back into the time domain to recover the approximate object image. The effectiveness of the DPFI algorithm is validated by comparing its results with those of polarized imaging and the traditional PFI.

We measure the PSF of the liquid crystal lens under different voltages, showing that the e-light’s focused spot is asymmetrical, indicating wavefront asymmetry in the lens. Using the DPFI algorithm, we conduct quantitative analysis on the imaging results of the ISO12233 resolution chart in both positive and negative lens states. The results show that the contrast of images from polarized imaging and the PFI algorithm is roughly similar in both lens states. However, compared to the PFI algorithm, the DPFI algorithm improves contrast by 22.3% and 98.9% in the positive and negative lens states, respectively. This improvement is partly due to the reduction of lens aberrations and the scattering effect of the liquid crystal material. Additionally, the DPFI algorithm performs better with the negative liquid crystal lens, as the object distance is greater, causing more concentrated scattered light in the center of the black stripe areas on the complementary metal oxide semiconductor (CMOS). Additionally, the DPFI algorithm performs better with the negative liquid crystal lens, as the object distance is greater, causing more concentrated scattered light in the center of the black stripe areas on the CMOS.

The DPFI method proposed in this study achieves polarization-free imaging for liquid crystal lenses. By measuring the PSF of the imaging system at different voltages and using these PSFs as variables in the DPFI algorithm, image restoration is achieved. The results from the resolution chart indicate that images processed with the DPFI algorithm exhibit better contrast and sharper edges compared to those processed with polarized imaging or the PFI algorithm. Furthermore, the DPFI algorithm optimizes high-frequency components more effectively. Although images processed by the DPFI algorithm exhibit higher noise levels than the original images, magnified details remain superior to those processed with the PFI algorithm. Overall, the DPFI algorithm offers significant advantages over the traditional PFI method.