Fig. 1. Concept of a unidirectional diffractive imager with partially coherent illumination. (a) Schematic of unidirectional imager under partially coherent, monochromatic illumination with a wavelength of λ. The unidirectional diffractive processor reproduces the input object’s image in the forward propagation direction (blue line from FOV A to FOV B), while suppressing the image formation in the backward propagation direction (brown line from FOV B to FOV A). This design includes four phase-only diffractive layers axially spaced by d, each containing 200×200 diffractive features that modulate the phase of the transmitted optical field. (b) Six sets of random phase profiles of partially coherent illumination, each containing Nϕtest phase profiles. Each set corresponds to one specific correlation length, Cϕtest, varying from ∼0.5λ to ∼3λ.

Fig. 2. Performance of a partially coherent unidirectional imager. (a) Physical layout of a four-layer unidirectional imager design. (b) Optimized phase profiles of the diffractive layers in a unidirectional imager trained with Nϕtrain=16 and Cϕtrain=2.5λ. (c) Blind testing results of the unidirectional imager with Cϕtrain=Cϕtest=2.5λ and Nϕtest=2048. The first three rows display the input amplitude objects, forward output images, and backward output images, all using the same intensity range. For comparison, the last row displays the backward output images with increased contrast. Note that both the forward propagation and backward propagation use the same input amplitude objects as displayed in the first row. (d)–(f) Performance evaluation of the diffractive unidirectional imager using 10,000 MNIST test images with PCC, diffraction efficiency, and PSNR metrics.

Fig. 3. Influence of Nϕtrain on the performance of partially coherent unidirectional imagers. (a)–(d) Performance analysis of partially coherent unidirectional diffractive imagers with Cϕtrain=Cϕtest=2.5λ, Nϕtest=2048, and different Nϕtrain values ranging from 1 to 64. The performance in each case was evaluated using 10,000 MNIST test images with PCC, diffraction efficiency, PSNR, and FOM metrics. (e) Examples of the blind testing results with different Nϕtrain values. The first three rows display the input amplitude objects, forward output images, and backward output images, all using the same intensity range. For comparison, the last row shows the backward output images with increased contrast.

Fig. 4. Influence of Cϕtrain on the performance of partially coherent unidirectional imagers. (a)–(d) Performance analysis of partially coherent unidirectional diffractive imagers with different Cϕtrain values ranging from ∼3.0λ to ∼0.5λ, where Cϕtest=Cϕtrain. The performance in each case was evaluated using 10,000 MNIST test images with PCC, diffraction efficiency, PSNR, and FOM metrics. The two-star markers in (d) represent the diffractive models with Cϕtrain=0.5λ and Cϕtrain=1.0λ, both of which were trained using a high-resolution image dataset composed of random intensity patterns. (e) Examples of the blind testing results with different Cϕtrain values ranging from ∼3.0λ to ∼0.5λ. The first three rows display the input amplitude objects, forward output images, and backward output images. For comparison, the last row shows the backward output images with different intensity ranges. Images with the same-colored frame share the same intensity range.

Fig. 5. Optimized phase profiles of the diffractive layers of different unidirectional imagers trained with varying Cϕtrain - from ∼0.5λ to ∼3.0λ.

Fig. 6. The generalization performance of unidirectional diffractive imagers across various Cϕtest values, ranging from ∼0.5λ to ∼3λ, despite being trained with a specific Cϕtrain.

Fig. 7. Image dataset external generalization for the unidirectional imager with Cϕtrain=Cϕtest=2.5λ. Blind testing results with EMNIST letters (a) and customized gratings (b), both of which were never used during training.

Fig. 8. Spatial resolution analysis for a unidirectional diffractive imager design with Cϕtrain=Cϕtest=2.5λ.