Experimental optical encryption with full complex modulation.

We present, to our knowledge, a novel method to achieve experimental encryption using double random phase encoding with full complex modulation and a single phase-only spatial light modulator. Our approach uses double phase encoding to generate phase-only holograms containing complex-valued input planes for a joint transform correlator (JTC) cryptosystem. This approach enables users to independently manipulate both the phase and amplitude of the cryptographic keys and objects, thereby significantly enhancing the versatility of the optical cryptosystem. We validate the capabilities of our proposed scheme by generating optimized random phase masks and using them to experimentally encrypt various grayscale and binary objects. The experimental complex modulation obtained with the system detailed in this work, in conjunction with optimized random phase masks, results in an enhancement in the quality of the decrypted objects during reconstruction. Both numerical simulations and experimental findings corroborate the effectiveness of our proposal.

Deep learning denoising diffusion probabilistic model applied to holographic data synthesis.

In this Letter, we demonstrate for the first time, to our knowledge, a holographic data synthesis based on a deep learning probabilistic diffusion model (DDPM). Several different datasets of color images corresponding to different types of objects are converted to complex-valued holographic data through backpropagation. Then, we train a DDPM using the resulting holographic datasets. The diffusion model is composed of a noise scheduler, which gradually adds Gaussian noise to each hologram in the dataset, and a U-Net convolutional neural network that is trained to reverse this process. Once the U-Net is trained, any number of holograms with similar features as those of the datasets can be generated just by inputting a Gaussian random noise to the model. We demonstrate the synthesis of holograms containing color images of 2D characters, vehicles, and 3D scenes with different characters at different propagation distances.

Color multilayer holographic near-eye augmented reality display.

This study demonstrates a full-color near-eye holographic display capable of superimposing color virtual scenes with 2D, 3D, and multiple objects with extended depth upon a real scene, which also has the ability to present different 3D information depending on the focus of the user's eyes using a single computer-generated hologram per color channel. Our setup makes use of a hologram generation method based on two-step propagation and the singular value decomposition of the Fresnel transform impulse response function to efficiently generate the holograms of the target scene. Then, we test our proposal by implementing a holographic display that makes use of a phase-only spatial light modulator and time-division multiplexing for color reproduction. We demonstrate the superior quality and computation speed of this approach compared with other hologram generation techniques with both numerical and experimental results.

Non-interferometric key recording applied to a joint transform cryptosystem.

In this Letter, we propose an opto-digital cryptosystem based on the joint transform correlator architecture without the need for a reference beam, phase-shifting techniques, or an additional window in the input plane. In this system, only two intensity recordings are necessary: the intensity of the key Fourier transform, and the joint power spectrum between the key and an arbitrary object in contact with a random phase mask. Combining them with the knowledge of their respective input modules, we implement a modified Gerchberg-Saxton algorithm to recover the phase associated with the encryption key. The validity of our approach is demonstrated by computer simulations and experimental results.

Improved phase hologram generation of multiple 3D objects.

We demonstrate the generation of phase holograms of multiple 3D objects at different axial positions without cross talk and significant improvements in performance over conventional methods. We first obtain the phase hologram of two 3D objects, each one comprising 50 layers, using the global Gerchberg-Saxton algorithm. Then, we discuss and demonstrate a propagation approach based on the singular value decomposition of the Fresnel impulse response function that enables fast computation of small distance propagations. Finally, we propose a new iterative hologram generation algorithm, to the best of our knowledge, that takes advantage of this propagation approach and use it to make the hologram of the same scene previously obtained with the global Gerchberg-Saxton algorithm. We perform numerical and experimental reconstructions to compare both methods, demonstrating that our proposal achieves 4 times faster computation, as well as improved reconstruction quality.

Alternative constraints for improved multiplane hologram generation.

In this work, we introduce a modified hologram plane constraint to improve the accuracy of the global Gerchberg-Saxton (GGS) algorithm used for multiplane phase-only hologram generation. This constraint consists of a modified phase factor that depends on the amplitude of the field in the hologram plane. We demonstrate that this constraint produces an increase in the mean correlation coefficient between the reconstructed planes from a multiplane hologram and the corresponding amplitude targets for each plane. Furthermore, this constraint can be applied together with a mixed constraint in the reconstruction planes, leading to a more uniform and controllable reproduction of a target intensity distribution. To confirm the validity of our proposal, we show numerical and experimental results for multiplane holograms with six discrete planes, using both high and low contrast targets. For the experimental results, we implement a holographic projection scheme based on a phase-only spatial light modulator.

Mixed constraint in global and sequential hologram generation.

In this paper, we implement a mixed constraint scheme with a global Gerchberg-Saxton algorithm for the improved generation of phase holograms from multiplane intensity distributions. We evaluate the performance of the proposed method compared to the mixed constraint sequential Gerchberg-Saxton algorithm, as well as the implementation of both schemes in several scenarios involving intensity distributions of up to nine independent planes. We also show that a careful selection of the parameters involved in the mixed constraint hologram generation technique can lead to even greater improvements in reconstruction quality. We present numerical results validating the effectiveness of our proposal.

Iterative multiplane hologram generation with mixed constraint.

In this work, we introduce a mixed complex and phase only constraint to the Gerchberg-Saxton (G-S) algorithm, leading to improvements in the generation of holograms from multiplane light field distributions. To achieve this, we determine the optimal weight factor for the complex and phase only part of a light field in every plane to achieve the best accuracy. We also demonstrate how this approach can be used to generate encrypted holograms that can only be reconstructed by illumination with a determined phase profile. In this way, we enable the possibility for secure, high-quality multiplane projection and display. We show numerical results for the generation of standard and encrypted seven-plane holograms, as well as the comparison with the conventional G-S algorithm.

Noniterative multiplane holographic projection.

In this paper, we introduce a mixed complex and phase-only constraint for noniterative computer generation of phase-only holograms from multiplane intensity distributions. We are able to reproduce three-dimensional intensity distributions with the same number of planes achieved with the Gerchberg-Saxton (GS) algorithm; at the same time, we maintain the fast computation time of a noniterative method. In this way, we enable the possibility of multiplane light field control in dynamic applications. We show numerical results for three- and eight-plane holograms, for different interplane distances-using either the same or different amplitude constraints in each plane. In all of these tests, our method results in a comparable or better reconstruction quality than the GS algorithm, while achieving a significant decrease in computing time. Finally, we experimentally demonstrate the capability of our proposal to achieve multiplane holographic projection.

Compression of 3D dynamic holographic scenes in the Fresnel domain.

In this paper we present an optodigital protocol for the compression of 3D dynamic scenes recorded with an off-axis Fresnel holographic system. The compression protocol involves optical scaling, sampling with binary masks, and multiplexing of the optical field data obtained after a filtering process applied to Fresnel holograms. Volume reduction of up to 93.71% and a 16-fold decrease in the transfer time are achieved. Virtual-optical reconstruction is performed for different values of the parameters involved in the compression protocol. The correlation coefficient is used as a metric to measure the loss caused by the volume reduction process. Furthermore, we show that a high level of lossy compression can be achieved with this protocol, with better reconstruction quality than the MPEG-4 video compression technique. Finally, we perform the experimental reconstruction using a holographic projection system based on a phase-only spatial light modulator, thus highlighting the potential of our proposal.

Optimized random phase tiles for non-iterative hologram generation.

In this work, we introduce a technique for fast, high-quality, non-iterative generation of phase-only holograms from both 2D and 3D scenes. In this technique, we generate an optimized random phase tile which behaves like a small diffuser, spreading the amplitude of a section of the scene throughout the hologram plane. Each section of the scene is multiplied by this tile and then propagated to the hologram plane by means of the Fresnel transform. The contribution from each tile is added, resulting in a phase-only hologram of the scene. The optimized random phase tiles can be generated for any distance between the hologram plane and the object using an iterative Fresnel algorithm. Afterwards, this tile can be used to generate holograms from any number of objects without the need for further iterative algorithms. These holograms present increased quality after reconstruction compared to similar non-iterative hologram generation techniques. Both numerical and optical experiments are carried out, demonstrating the effectiveness of our proposal.

Synthetic amplitude for improved reconstruction of noniterative phase holograms.

In this paper, we show how a specially designed synthetic amplitude can be used to obtain greatly improved reconstruction of objects only using the phase data of their Fourier or Fresnel transforms. The reconstruction of objects from phase-only information is of interest because phase modulation has much higher efficiency than amplitude modulation and can be achieved with a high degree of precision with current liquid-crystal-on-silicon spatial light modulators. However, direct reconstruction of an object from its phase information usually results in severely degraded outputs. Due to this issue, to achieve optimal reconstruction, the object information must be codified in a phase hologram by means of time-consuming algorithms. To avoid these kinds of algorithms, we propose using a synthetic amplitude, designed in such a way that, when multiplied with the phase information of the object, leads to high-quality reconstruction. This synthetic amplitude contains no information about the object and can be used to reconstruct a number of different inputs without further processing. We present experiments carried out in virtual and actual optical systems verifying the validity of our proposal for 2D, 3D, and dynamic scenes.

Optimized random phase encryption.

We propose for the first time, to the best of our knowledge, the use of optimized random phases (ORAPs) in a double random phase encryption scheme (DRPE). In DRPE schemes the convolution between two random phase functions encrypts the information to be secured. However, in actual encryption applications, this convolution of random phases also results in unwanted effects like speckle noise. In this Letter we show that under certain conditions this noise can be drastically reduced. These conditions can be easily achieved by using ORAPs. These ORAPs, besides containing information about the parameters of the optical system and maintaining all the security properties of a random phase function, ensure that the encrypted data is a phase-only function. This leads to a great increase in system performance, with decryption quality similar to the reconstruction of a phase-only hologram generated with the Gerchberg-Saxton algorithm. We show both numerical and experimental results confirming the validity of our proposal.

Optimized random phase only holograms.

We propose a simple and efficient technique capable of generating Fourier phase only holograms with a reconstruction quality similar to the results obtained with the Gerchberg-Saxton (G-S) algorithm. Our proposal is to use the traditional G-S algorithm to optimize a random phase pattern for the resolution, pixel size, and target size of the general optical system without any specific amplitude data. This produces an optimized random phase (ORAP), which is used for fast generation of phase only holograms of arbitrary amplitude targets. This ORAP needs to be generated only once for a given optical system, avoiding the need for costly iterative algorithms for each new target. We show numerical and experimental results confirming the validity of the proposal.

Experimental optical encryption of grayscale information.

In this paper, we present a new protocol for achieving lower noise and consequently a higher dynamic range in optical encryption. This protocol allows for the securing and optimal recovery of any arbitrary grayscale images encrypted using an experimental double random phase mask encoding (DPRE) cryptosystem. The protocol takes advantage of recent advances that help reduce the noise due to the correlation of random phase mask in the decryption procedure and introduces the use of a "reference mask" as a reference object used to eliminate the noise due to the complex nature of the masks used in experimental DRPE setups. This noise reduction increases the dynamic range of the decrypted data, retaining the grayscale values to a higher extent and opening new possible applications. We detailed the procedure, and we present the experimental results, including an actual experimental video of a grayscale scene, confirming the validity of our proposal.

Three-dimensional joint transform correlator cryptosystem.

We introduce for the first time, to the best of our knowledge, a three-dimensional experimental joint transform correlator (JTC) cryptosystem allowing the encryption of information for any 3D object, and as an additional novel feature, a second 3D object plays the role of the encoding key. While the JTC architecture is normally used to process 2D data, in this work, we envisage a technique that allows the use of this architecture to protect 3D data. The encrypted object information is contained in the joint power spectrum. We register the key object as a digital off-axis Fourier hologram. The encryption procedure is done optically, while the decryption is carried out by means of a virtual optical system, allowing for flexible implementation of the proposal. We present experimental results to demonstrate the validity and feasibility of the method.

Relación entre los terceros molares y el apiñamiento anterior inferior / Relationship between third molars and anterior inferior crowding

Este trabajo tuvo como fin aportar otro estudio a la controversia que existe sobre la relación de los terceros molares y el apiñamiento anterior inferior, ya que varios autores han planteado que sí existe una relación entre los terceros molares y la presión mesial que ejercen al erupcionar causando apiñamiento anterior. En contraposición, otros autores rechazan dicha relación. Se realizó una investigación de tipo descriptivo transversal en la cual se analizó si existieron cambios en la longitud de arco con la extracción de los terceros molares. La investigación se realió teniendo en cuenta una muestra de 15 pacientes entre los 20 y 25 años de edad, quienes formaban parte de una muestran anterior de ochenta pacientes de un trabajo de investigación realizado por Villamil, Ruiz, Guzmán y Martínez en 1993. Los pacientes tuvieron extracción quirúrgica de los terceros molares inferiores y las muestras fueron tomadas en un período de un año post exodoncia. Se tomaron modelos de estudio, radiografías laterales de cráneo y el componente anterior de fuerzas (CAF), para analizar el grado de apiñamiento en el momento del corte, comparado con el grado de apiñamiento encontrado anteriormente a la extracción. Los resultados encontrados, de acuerdo con el análisis estadístico utilizado, fueron los siguientes: sí existe una variación del índice de regularidad y el CAF, posterior a la cirugía de los terceros molares, disminuyó según la variación de los promedios