Patent ID: 12248137

DETAILED DESCRIPTION OF HE INVENTION

The present invention discloses a method for phase modulation based on the spatial, coherent addition of two (or more) electromagnetic fields, although, for the sake of simplicity, henceforth we only consider the sum of two fields:
E1(x,y)+E2(x,y)=ET(x,y)
where E(x,y)=A(x,y)·e−iφ(x,y), A(x,y) represents the amplitude of the field, which in the case considered herein does not vary spatially (A(x,y)=A), and φ(x,y) the spatial phase distribution, or phase map. Subscripts 1, 2, T, represent the first and second fields to be added, and the total field, respectively.

Thus, we find that the total field ET(x,y) is:
ET(x,y)=A1·e−iφ1(x,y)+A2·e−iφ2(x,y)=AT·e−iφT(x,y)
where φT(x,y)=φ1(x,y)+φ2(x,y) is a spatial sum of phasors. Since the amplitude of both fields is constant, only the sum of the phase term is relevant, so henceforth we refer to the sum of electromagnetic fields as the sum of phase maps.

With this method any phase map can be replicated, for instance, using modulators with a low birefringence coefficient (i.e. a lower dynamic range of phase modulation), which are usually faster and cheaper.

To ensure that the sum of the phase maps is exact and no additional terms are being added as a result of the propagation of the wavefront it is important that both phase maps are in conjugate planes. In the preferred configuration of the invention, these conjugate planes coincide with the pupil planes of the system.

This method can be carried out essentially in two different configurations: using two modulators1,7in series and having the optical path pass once through each (FIG.1), or using a single phase modulator8,14with its active area divided into two halves and having the optical path pass once through each half (FIGS.2and3).

In particular, the preferred form of the present invention discloses a phase mapping system where two spatial light modulators1,7are used, arranged in series, where the optical path passes once through each (FIG.1). Between both modulators1,7, an optical unit magnification system combines the plane of the first modulator2with that of the second modulator6, enabling the phase maps to be precisely and rigorously added together.

The control of the total phase map generated (φT(x,y)) is carried out by means of software. Phase maps can be calculated to represent primary or higher-order aberrations, with special interest in ophthalmic applications and adaptive optics; or by computer-generated holograms or CGH (Computer Generated Holography), with possible applications in virtual reality or photolithography systems among others. In any case, once the phase map is calculated, represented between 0 and 2π radians, we divide it by two, to distribute it between the two modulators (or two halves), according to the configuration.

The way to distribute the total phase to be modulated between the two modulators (or two halves in a single modulator) can be done essentially in two ways: i. Dividing the total phase to be modulated by two and displaying the same value in each of the modulators

(i.e.,φ1(x,y)=φ2(x,y)=φr(x,y)2)
or ii. Using one modulator solely to display phase values up to its maximum modulation capacity and the second modulator to display the rest of the phase needed to generate the complete phase map.

There are two main configurations in which the system can be organized: i. The two phase modulators1,7(or the two halves of the same modulator8) can be in planes conjugated to each other, incorporating an optical system between them, as shown inFIGS.1and2; or ii. Forming the image of one device on the other by means of a lens16, without both planes being necessarily conjugated to each other, as portrayed inFIG.3, if the extra phase generated by not conjugating planes is subsequently corrected by software. A preferred configuration of the invention is portrayed inFIG.1and will be detailed below.

FIG.2shows one of the options for implementing the present invention. It entails using a single modulator8with its active area divided into two halves and independently controlled by software. The planes of each half9,12are conjugated to each other by means of a double passage through a lens10and a mirror11. This scheme is more compact and less costly, since only one modulator8and one lens10are used to make up the telescope. However, the alignment between the two phase maps in the exit pupil plane is exacting. The right-hand panel ofFIG.4illustrates the coincidence of pupils of a wrapped phase after optimal alignment. This system is highly sensitive to lens rotation and offsets (lens10, inFIG.2), asymmetrically blurring one phase map with respect to another, as shown in the left-hand panel ofFIG.4. Non-optimal alignment can add artifacts and noise to the diffraction pattern and the images through the system, although the possibility exists of compensating for this by means of software.

Another of the experimental configurations designed is outlined inFIG.3. In this configuration, as in that outlined inFIG.2, a single modulator14is used, and this could be made even more compact than that described above, thanks to the use of two beam splitter cubes13,18, ensuring the normal incidence on the two halves of the modulator14and on the lens16that connects them, thanks to the two mirrors15,17at459that redirect the optical path, reducing the possibility of the appearance of asymmetric blurring at the conjugate pupils (FIG.4, left). In addition to the components detailed above, a screen19is added that blocks the light transmitted by the beam splitter13to the point of entry, in order to prevent undesired reflections. In this case, the lens16may form the image of the first half on the second with a unit magnification if the distance between said lens16and the halves of the modulator14is twice its focal length. If this requirement is not met, the two halves would not be conjugated, and an additional spherical wavefront generated by the propagation of the wavefront would need to be compensated by means of software, as indicated in the paper by Goodman, Joseph W, introduction to Fourier optics. Roberts and Company Publishers, (2005).

FIG.1portrays an experimental configuration of the method described, using two modulators1,7and an optical telescope formed by two lenses3,5and a mirror4conjugating the pupil planes2,6between them.

InFIG.2, the experimental system presented enables the use of the method described using a single modulator8, where the different areas of the device9,12are conjugated to each other by a telescope thanks to a double passage through a lens10and a mirror11.

FIG.3portrays a more compact arrangement of the system in which a single lens16forms the image of the first half on that of the second. The beam bears on the first half of the modulator14in normal incidence by means of a beam splitter13, while the beam transmitted is blocked by a screen19. The beam reflected by the modulator14is redirected by two mirrors15,17at 45 degrees to ensure its normal incidence on the lens16and the second half of the modulator14. A second beam splitter18returns the modulated beam in the same direction of entry.

FIG.4shows two images of the pupil plane coinciding with the plane of the two modulators1,7(in the preferred experimental configuration of the invention, outlined inFIG.1), where a 2D blur has been generated. In the panel on the left it may be seen how one of the modulators coincides with the pupa plane and is well defined in its entirety, while this is not the case with the second modulator, where the horizontal direction is slightly out of focus, in addition to being displaced one from the other. The optimal situation of the experimental system is portrayed in the right-hand panel, where both phase maps coincide entirely and are well-defined throughout.

FIG.5compares the experimental modulation results, obtained with a standard phase modulator with a modulation depth of 2π radians, and two modulators1,7with a modulation depth of approximately π radians in the configuration shown inFIG.1. The first two rows compare the point spread functions (PSFs) obtained with the different aberrations generated and specified in the columns (D: Blur, A: Astigmatism, C: Comma, E: Spherical aberration). The units of blur and astigmatism are dioptres (D) and those of comma and spherical aberration, micrometers (μm). The last row shows the image formation of a visual stimulus when the aberrations specified in the different columns have been generated with a standard modulator whose modulation depth is 2π radians, and then corrected by the modulation system described herein, wherein the planes of the modulators1,7are conjugated.

The following numerical references are associated with the different elements that integrate the invention and its embodiments:1. Spatial light modulator.2. Pupil plane in the first modulator.3. System lens.4. Mirror.5. System lens.6. Pupil plane in the second modulator, conjugated with2.7. Spatial light modulator.8. Spatial light modulator.9. Pupil plane at the first part of the modulator.10. System lens.11. Mirror.12. Pupil plane at the second part of the modulator, conjugated with9.13. Beam splitter.14. Spatial light modulator.15. Mirror.16. Lens.17. Mirror.18. Beam splitter.19. Beam blocking screen.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

A preferred embodiment of the invention is shown schematically inFIG.1. It consists of a system for adding two identical and spatially coincident phase maps. This is achieved by the use of two spatial light modulators1,7located in optically conjugated planes2,6. These planes are conjugated by means of a unitary magnification telescope formed by two lenses3,5and a mirror4.

A crucial condition for the proper implementation of the present invention is that the phase maps of the individual modulators1,7coincide spatially. This can be verified by forming an image of the exit pupil of the system with a camera, while showing a wrapped phase map at the modulators1,7. A primary alignment consists of the physical movement of the devices, subsequently to achieve fine alignment by means of the digital manipulation of the phase maps. While the coincidence of the outlines of the wrapped phase maps ensures transverse alignment, a similar, thin thickness thereof ensures axial coincidence. An example of this coincidence is shown in the right-hand panel ofFIG.4. The opposite case, without transverse and axial coincidence, is shown in the left-hand panel ofFIG.4.

Within this configuration of the invention, inFIG.5we show, by way of an example, different Point Spread Functions (PSFs) of phase maps of primary aberrations, (blur, astigmatism, comma, or spherical aberration), of great interest in visual optics. The first row ofFIG.5portrays the PSFs corresponding to various combinations of these aberrations, obtained with a standard phase modulator capable of modulating the entire phase range of 2π, and in the second row, the PSFs of the same aberrations, but generated with two phase modulators1,7with a modulation depth limited to approximately π radians, using the configuration described herein. In the third row, images of a visual test are shown where the same aberrations defined in each column have been generated by the standard modulator and corrected by the two modulators1,7in the configuration described and outlined inFIG.1.

Operation of the instrument is possible provided that modulation exists (i.e., that the modulation of the modulators or active modulation areas is greater than 0 radians). The final operation depends on whether a modulation of 2π can be achieved. If the modulators modulate up to π, two modulators are sufficient. If the modulators modulate π/2, four would be required, etc. The more modulators are employed, the more complicated the system will be to execute experimentally and some efficiency may be lost, but it is still possible.

Although some embodiments of the invention have been described and represented, it is clear that modifications may be introduced to them within the scope of the same, and that the invention should not be considered limited to these embodiments, but only to the content of the following claims.