Performance evaluation of extended depth of field microscopy in the presence of spherical aberration and noise

Abstract

Effectiveness of extended depth of field microscopy (EDFM) implementation with wavefront encoding methods is reduced by depth-induced spherical aberration (SA) due to reliance of this approach on a defined point spread function (PSF). Evaluation of the engineered PSF's robustness to SA, when a specific phase mask design is used, is presented in terms of the final restored image quality. Synthetic intermediate images were generated using selected generalized cubic and cubic phase mask designs. Experimental intermediate images were acquired using the same phase mask designs projected from a liquid crystal spatial light modulator. Intermediate images were restored using the penalized space-invariant expectation maximization and the regularized linear least squares algorithms. In the presence of depth-induced SA, systems characterized by radially symmetric PSFs, coupled with model-based computational methods, achieve microscope imaging performance with fewer deviations in structural fidelity (e.g., artifacts) in simulation and experiment and 50% more accurate positioning of 1-μm beads at 10-μm depth in simulation than those with radially asymmetric PSFs. Despite a drop in the signal-to-noise ratio after processing, EDFM is shown to achieve the conventional resolution limit when a model-based reconstruction algorithm with appropriate regularization is used. These trends are also found in images of fixed fluorescently labeled brine shrimp, not adjacent to the coverslip, and fluorescently labeled mitochondria in live cells.

Point spread function engineering based on wavefront phase modulation

“…The optimal parameters of the phase mask need to be optimized based on the aberration invariance of the system in the spatial domain (PSF) or frequency domain (OTF). After determining the phase mask type, one way to calculate the PSFs/OTFs is using a diffraction limited aberration-free imaging system 26,78,81,[96][97][98] . This approach facilitates versatile, fast phase mask design.…”

“…In order to suppress the noise in the reconstructed image, a series of nonlinear and regularized deconvolution algorithms are introduced 82,98,[109][110][111] , and the deconvolution algorithm based on deep learning shows better performance 68,78,112 . However, all these deconvolution algorithms assume that the blur kernel is shift-invariant, which is obviously not in line with the shift characteristics of real optical systems and will lead to artifacts in the reconstructed image 113 .…”

“…When the sample thickness or surface undulation is greater than the DOF, multi-refocusing are needed to acquire a clear image of the entire sample, which significantly increases the operational difficulty and imaging time. EDOF microscopy based on wavefront coding 26,78,80,81,85,97,98,106,122 can achieve DOF extension up to 10×, which greatly simplifies the sample preparation and imaging process. In addition, as a small aberration system, the microscope can be modeled as a diffraction-limited system, which is very suitable for wavefront coding modification.…”

“…In contrast, the wavefront coding infrared imaging system do not require compensating structures and have the advantage of simplicity and low cost 99,131 , and can also simultaneously suppress other aberrations 100 . In addition to infrared imaging systems, wavefront coding can suppress aberrations in zoom systems and simplify mechanical structures 132,133 , increase the aberration tolerances of astronomical optical systems 92 , suppress the coma and astigmatism of off-axis three-mirror anastigmatic optical systems 94,101,108 , suppress dynamic aberrations of conformal optical system using fewer components 86,95,127 , and suppress spherical aberration caused by refractive index mismatch in microscopes 79,96,98 . And Wavefront encoding can also protect the imaging system from high-irradiance lasers with the help of large-area PSFs that disperse the optical energy 134,135 .…”