Assuming far field imaging, each point in the scene produces a plane wave which passes through the diffraction grating and propagates onto the sensor using Fresnel diffraction.

The image is formed by calculating the propagation from all points in the scene as well as considering shot and read noise on the sensor.

The propagation process can be modeled as a matrix vector product where the matrix stores the diffraction grating responses for all possible points of incoming radiation in the scene.

Description of the main geometric characteristics of phase-antisymmetric gratings.

Description of the main characteristics of spiral phase-antisymmetric gratings. They produce a wide point spread function instead of focusing the incoming radiation.

Phase delay and structural characteristics for each one of the studied optical elements. All three elements were optimized for a wavelength of λ = 500 nm keeping the same aperture size, focal length and refraction index of the propagating medium. A phase delay of π is imposed by the gratings while the lens provides a continuous range of phase delays based on its curvature. Note that, phase delay color coding is to be understood as modulo π for the lens.

During propagation we consider light attenuation. Reconstruction is performed using baseline Tikhonov regularization.

Visual performance comparison for the reconstruction of the Mona Lisa image under low noise and different wavelengths. Reconstruction was performed using the response of each optical element for each one of the different wavelengths (400, 500 and 600 nm).

Visual performance comparison for the reconstruction of the Mona Lisa image under high noise and different wavelengths. Reconstruction was performed using the response of each optical element for each one of the different wavelengths (400, 500 and 600 nm).

Peak signal to noise ratio (PSNR) performance comparison for the reconstruction of the Mona Lisa image under varying levels of noise and different wavelengths. Reconstruction was performed using the response of each optical element for each one of the different wavelengths (400, 500 and 600 nm).

Visual performance comparison for the reconstruction of a QR code image under low noise and different wavelengths. Reconstruction was performed using the response of each optical element for each one of the different wavelengths (400, 500 and 600 nm).

Visual performance comparison for the reconstruction of a QR code image under high noise and different wavelengths. Reconstruction was performed using the response of each optical element for each one of the different wavelengths (400, 500 and 600 nm).

Peak signal to noise ratio (PSNR) performance comparison for the reconstruction of a QR code image under varying levels of noise and different wavelengths. Reconstruction was performed using the response of each optical element for each one of the different wavelengths (400, 500 and 600 nm).

Visual performance comparison for the reconstruction of the Mona Lisa image under low noise and different wavelengths. Reconstruction was performed using the response of each optical element for a wavelength of 500 nm.

Peak signal to noise ratio (PSNR) performance comparison for the reconstruction of the Mona Lisa image under varying levels of noise and different wavelengths. Reconstruction was performed using the response of each optical element for a wavelength of 500 nm.

Visual performance comparison for the reconstruction of a QR code image under high noise and different wavelengths. Reconstruction was performed using the response of each optical element for a wavelength of 500 nm. Note that the reconstructed QR code using the spiral gratings is detectable by a conventional QR code reader.

Peak signal to noise ratio (PSNR) performance comparison for the reconstruction of a QR code image under varying levels of noise and different wavelengths. Reconstruction was performed using the response of each optical element for a wavelength of 500 nm.