Plenoptic light field reconstruction and wavefront sensing based on measuring optical path difference are well known achromatic wavefront reconstruction techniques: http://www.cafadis.ull.es/

My sugestion of the last century: https://arxiv.org/pdf/0904.2598.pdf

has experimental demonstration made on this century. For the moment only in Portughese: http://www.ifi.unicamp.br/~lunazzi/F530_F590_F690_F809_F895/F530_F590_F690_F895/F530_F590_F690_F895_2011_sem2/HenriqueG-Lunazzi_RF1_F530.pdf

I want very soon to prepare the results (which includes the experiment of the reconstruction of two small white light sources) as an article in english.

Dear Jose,

Your paper 1993 is very interesting. However, it seems that the other mechanism than the one discussed in the papers mentioned in my question is used in it.

Hi Anatoly,

Thank you for your information. I need to read these materials carefully.

I see, your question was for a specific mechanism, which has a general description name, not one specific. That is why I derived to a different one, also a non-holographic mechanism of achromatic wavefront reconstruction.

Hi Anatoly,

You could think of using polychromatic phase retrieval algorithms for polycolor wave-front reconstruction. See for example the publication by Batey et. al. used ptychography:

Article Information multiplexing in ptychography

This is formulated as an inverse problem: Find the monochromotic wavefronts of a set of polychromatic measured diffraction intensities (or similarly interferogram). (ptychography uses data redundancy to solve for the phase, where holography uses an external reference. the data redundancy is provided by an overlapping scanning scheme)

This could also used for synthesis problems, where the goal is to design achromatic optical elements: Find optical elements that shape the monochromatic wave fronts so as to yield a desired intensity distribution.

I hope I understood your question correctly. :)

Best wishes,

Lars

Hi Lars, Thank you for answer. Your information is new for me.

Dear Jose, Sure, all methods of the non-holographic wavefront reconstruction are interesting for me. But I compare their mechanisms with the one mentioned in my question.

Hi Anatoly,

You may also want to read Ren Ng's PhD thesis on digital light field photography he defended at Stanford University in 2006 and other publications by Lytro, a company that Ren founded the same year: https://support.lytro.com/hc/en-us/articles/200863650--Lytro-Founder-Ren-Ng-s-PhD-dissertation

Anatoly, thank you for this link. I just tried to find Ren Ng's PhD thesis. It is remarkable that the idea of Lippmann integral photography has now a practical application. It is the second brilliant idea of Gabriel Lippmann that found its use after a long delay. The first one is the idea of Lippmann color photography, which is used in volume holograms. I hope that once in future the idea of Yuri Denisyuk of wavefront reconstruction based on a geometric-optical reflection of reconstructing radiation from surfaces with constant phase differences between the object and reference waves [1] will also find its use. Here it is necessary to note that this mechanism does not work in Denisyuk (also called Lippman–Bragg) holograms. This was shown in [2, 3].

1. Yu. N. Denisyuk, “On the reflection of optical properties of an object in the wave field of the radiation scattered by it,” Sov. Phys. Dokl. 7, 543–545 (1962).

2. https://www.researchgate.net/publication/320471999_On_Two_Image-Forming_Mechanisms

3. https://www.researchgate.net/publication/252543766_Geometric-optical_reconstruction_of_a_wavefront

In Chapter 4 of https://www.researchgate.net/publication/6726807_Achromatic_optical_elements a combined approach to wavefront reconstruction is discussed. According to this the production process of the optical element for the object wavefront reconstruction is divided into the following stages:

1. Measurement of a 2D distribution of the object field on some surface.

2. Calculation of the 3D object field and the shape of surfaces with constant phase differences corresponding to interference of the object field with the virtual GO wave having the eikonal equaled to the eikonal of the reconstructing wave.

3. Fabrication of the optical element.

I suppose that the methods mentioned here by colleagues (plenoptic camera or ptychography) can be used in this process at stage 1.

For me the most interesting option is the wavefront reconstruction including direct recording of the interference fringe structure in the medium bulk. The problem is in recording of only few periods of the interference fringe structure. The ideal is obtaining of an isolated surface with constant phase differences between the object and reference waves [1]. Firstly we tried to use the low coherent light source like a high pressure mercury lamp for recording [2]. Then we used the femtosecond laser for this [3]. The other problem is a necessity in extremely thick recording medium. We used the silver halide emulsion or the dichromated gelatin with thickness up to 300 μm. The great medium thickness is not necessary for 2D analog of the achromatic wavefront reconstruction in the plane waveguides [4]. However, I am confident that some other possibilities of recording will be found in future. It can be: a) Recording by short acoustic pulses. Here the pulse duration can be substantially longer due to the difference in the velocity of sound and light. In principle, the reconstruction is possible both by acoustic and electromagnetic waves. b) Using of the threshold recording medium. In principle, this allows to record the area of pulses intersection without interference. c) Using of recording medium, which allows the two different electron transitions. In this case two oppositely directed light pulses should have different wavelengths corresponding to these electron transitions. This process can form a solitary interface [1] between two states of recording medium with different refraction indexes. d) Maybe using of some hand-made recording media similar to photonic crystals of metamaterials is possible.

1. K. A. Stetson, “What is a hologram,” Laser Focus 3(5), 25–29 (1967).

2.https://www.researchgate.net/publication/238909233_Geometric-optical_reconstruction_of_a_wavefront_experimental_realization_with_femtosecond_laser_pulses

3.https://www.researchgate.net/publication/257830609_Achromatic_reconstruction_of_the_wave_front_of_femtosecond_laser_pulses

4.https://www.researchgate.net/publication/23387611_Achromatic_reconstruction_of_femtosecond_holograms_in_the_planar_optical_waveguide

My previous comment can be considered as a program of future experimental research in this direction for anybody who is interest in it. Now I can suggest the question for theoretical study. This is a problem: what types of fields could be reconstructed by geometric-optical mechanism? It is clear that this is not arbitrary field. We tried to make a first step in this direction at the end of [1]. However, this is just the first step only.

1.https://www.researchgate.net/publication/320471999_On_Two_Image-Forming_Mechanisms

Recently I posted the project Achromatic wavefront reconstruction https://www.researchgate.net/project/Achromatic-wavefront-reconstruction?_sg=Pv-cBZ1ph-xcLw4N-VqFkGXUzJhq9-XQOlaWsTQXK3E5dI8BsCEVkNRvI1rbfkVyPKHoKdOJhujIoyOsjcZXcRPXOmpjR0KjJeEj , which subject is connected with this discussion.