The Plenoptic Camera as a wavefront sensor for the European Solar Telescope (EST)

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1 The Plenoptic Camera as a waveront sensor or the European Solar Telescope (EST) Luis F. Rodríguez-Ramos* a, Yolanda Martín a, José J. íaz a, J. Piqueras a, J. M. Rodríguez-Ramos b a Institute o Astrophysics o the Canary Islands, Tenerie, SPAIN b University o La Laguna, Tenerie, SPAIN ABSTRACT The plenoptic waveront sensor combines measurements at pupil and image planes in order to obtain waveront inormation rom dierent points o view simultaneously, being capable to sample the volume above the telescope to extract the tomographic inormation o the atmospheric turbulence. Ater describing the working principle, a laboratory setup has been used or the veriication o the capability o measuring the pupil plane waveront. A comparative discussion with respect to other waveront sensors is also included. Keywords: adaptive optics, atmospheric turbulence tomography, solar adaptive optics, plenoptic camera 1. INTROUCTION The plenoptic waveront sensor, also known as the plenoptic camera or the CAFAIS camera, was originally created to allow the capture o the Light Field (LF) [1], a concept extremely useul in computer graphics where most o the optics are treated using exclusively the geometric paradigm. Basically the Light Field is a our-variable volume representation o all rays and their directions, and thus allows the creation by synthesis o the image as seen rom virtually any point o view. The history o the search or this description is really old, and reerences can be ound in the very early beginning o the twentieth century, where F. Ives (1903) described a system with an array o pinholes at the ocal plane or Lippmann (1908) Nobel prize laureate who described the irst Light Field capturing device [2][3]. Modern light ield description was stated by Adelson and Wang (1992)[4], and a signiicant step orward was done by Ren Ng (2005) [5] who built a working system and established a our-dimensional Fourier view o the imaging process. Recently, Georgiev (2009)[6] has introduced a number o diraction considerations and deined the plenoptic camera 2.0. The use o the plenoptic (CAFAIS) camera or real-time 3 cameras has been patented at the University o La Laguna (Spain) by one o the authors [7], exploiting the capability o reocusing at several distances and selecting the best ocus as the distance to the object. The use o plenoptic optics or waveront measurement was described by Clare and Lane (2005) [8], or the case o point sources. We describe in this paper the use o the plenoptic camera as a waveront sensor, especially adequate or computing the tomography o the atmospheric turbulence or adaptive optics in solar telescopes. Ater a description o the sensor and the required processing, the results o laboratory tests are presented, which clearly show the viability o the system or pupil plane waveront measurement. 2. ESCRIPTION OF THE PLENOPTIC WAVEFRONT SENSOR A microlens array with the same -number than the telescope is placed at its ocus (ig 1), in such a way that many pupil images are obtained at the detector, each o them representing a slightly dierent point o view. The use o the same - number guarantees that the size o the image o the pupil is as big as possible, without overlapping with its neighbor, providing thus optimum use o the detector surace. An example o a plenoptic image obtained at the Vacuum Tube Telescope (VTT, Canary Islands, Spain) is shown in ig. 2, depicting an array o 15x19 microlenses imaged on a 1024x1280 ueye CMOS Camera. The spider support or the secondary mirror can be easily identiied, together with some vignetting at the lower let side, created by the telescope coniguration at the moment o the data acquisition. *lrr@iac.es; phone ; ax ;

2 In order to understand the behavior o the plenoptic waveront sensor, it is important to identiy the direct relationship existing between every pupil point and its corresponding image or each microlens. As shown in ig 3, every pupil coordinate is imaged through each microlens in a way that all rays passing through the indicated square will arrive to one o the pupil images, depending only on the angle o arrival. This act clearly indicates that the image that would be obtained i the pupil were restricted to this small square can be reconstructed by post-processing the plenoptic image, selecting the value o the corresponding coordinate at every microlens and building an image with all o them. I diraction considerations are introduced in addition to geometric optics, as stated by Clare and Lane [8], the image obtained using this post-processing is really the result o the convolution o the geometric image with the transer unction o the microlens, which basically implies a low pass blurring equivalent to the well known diraction limiting eects ound when imaging through a inite aperture. These eects however will be neglected along this article except when evaluating the maximum resolution attainable in the pupil plane waveront measurement. Telescope Microlens Array etector Fig. 1. Outline o the plenoptic camera used as waveront sensor. A microlens array is located at the telescope ocus, instead o in some pupil plane as required or the Shack-Hartmann () sensor. I the -numbers o both telescope and microlens are the same, the detector will be illed up with images o the pupil o maximum size without overlapping. With this scheme, both pupil and image planes are sampled simultaneously, and later processing may extract relevant inormation coming rom the volume above the telescope. The simplest case is the waveront at the pupil, which can be extracted rom the relative displacement o the recomposed images rom every pupil coordinate, speciically or solar adaptive optics, in the ollowing way: a) To compensate the plenoptic image rom zero-level and dierential pixel response (bias and lat), using calibration inormation regarding the optical and electronics system. b) To generate the images corresponding to every pupil coordinate, using the resolution and/or iltering adequate to the desired sampling scheme. c) To compute the cross-correlation o every image with respect to one o them, in order to evaluate the relative average tilt o the pupil plane waveront. The position o the peak o the correlation is computed with sub-pixel resolution using quadratic interpolation between the maximum correlation value and its neighbors. d) To estimate the phase surace rom the local derivatives using a suitable algorithm, like the Hudgin iterative reconstructor. [See J. íaz et al, this conerence].

This arrangement will be especially useul when extended objects are imaged, and the case o solar granulation will be speciically addressed. Fig. 2.

3 This arrangement will be especially useul when extended objects are imaged, and the case o solar granulation will be speciically addressed. Fig. 2. Example o plenoptic image o the Sun on a plenoptic camera o 19 x 15 microlenses, using a detector o 1280 x 1024 pixels at the VTT telescope (Observatorio del Teide, Canary Islands, Spain) : : Fig. 3. Correspondence between pupil and pupil images. Every pupil coordinate is re-imaged on the corresponding position o each pupil image, depending on the arriving angle o the incoming ray.

4 3. PUPIL PLANE RESOLUTION LIMIT It is well known that at least an aperture in the range o milimeters is needed to obtain a reasonably good image o the solar granulation, which will be used as a correlation guide or estimating image displacements and then converted to waveront tilts. When a Shack-Hartmann () waveront sensor is used, this limit will directly impose a maximum resolution level in the pupil waveront measurement, due to the act that no more than N = subpupils can be allocated at the system entrance diameter, i solar granulation is expected to be present at the resulting subpupil image. (Let be the telescope diameter and the minimum aperture acceptable to have solar granulation in the image). This number could become a serious limit when the adaptive optics tries to reach superb working igures, because it will aect directly at the quality o the reconstruction (or the AO overall igures) governing the itting error o the measured waveront. This limit will turn on a maximum o 7 waveront pupil samples (in diameter) in a telescope like VTT (Teide Observatory), or 40 in a 4-m telescope (EST). In order to check i the plenoptic waveront sensor could be used to overcome this limitation, the maximum resolution achievable will be analysed in this section. (1) Solar granulation inormation is located at high spatial requencies, with very low contrast unortunately. An optical imaging system with a minimum bandwidth is needed to provide suicient throughput at those spatial requencies, being this bandwidth represented by the cut-o requency o the optical transer unction o the circular aperture. This cut-o spatial requency is [9]: ρ c = (2) λ Being the aperture, λ the wavelength o the light and the ocal length o the imaging system. In our case, the value o the cut-o requency adequate or the solar granulation will be given by the speciic values o (maximum aperture) and T (Telescope ocal length): ρ c = (3) λt As described previously, the virtual image corresponding to any aperture can be synthesized rom the plenoptic image by selecting one pixel rom each microlens. In order to have some level o solar granulation to correlate with, these spatial requencies shall be present and adequately sampled, in a similar way that would happen to a sensor. Using the Shannon theorem, correct representation o the solar granulation spatial requencies will require a sampling o twice these requencies (2ρ c ) and thus will impose a limit on the separation o the microlenses: The microlenses should not be separated at the ocal plane by more than 1/2ρ c meters (or microns) and thus they can not be bigger than this size. 1/2ρ c. Fig. 4. The synthesized image is built ater selecting one pixel rom every microlens. High spatial requencies containing granulation inormation will only be present at the reconstructed image i the separation between microlenses is less than 1/2ρ c, being ρ c the spatial requency o the solar granulation.

5 Using this scheme, it can be easily shown that the maximum microlens size is related to the minimum subpupil by: 1 λ T = = (4) 2ρc 2 Looking at the expression giving the maximum µl (4), it should be concluded that a bigger ocal length will allow or bigger microlenses and thus better pupil imaging, because the image o the pupil will also be aected by the resolution limit blurring, as shown next. Considering now the propagation through the microlenses, using again the system transmission o a circular aperture, the maximum available spatial requency at the pupil plane will be µl = (5) F c λ µl And thus the sampling pitch at the pupil plane needed or grasping all the inormation available will be (double): δ λ pupil = (6) 2µ L Being this time the microlens ocal length and its diameter the parameters o the equation. Substituting the microlens diameter previously calculated, the maximum pupil sampling can be obtained, i.e, the minimum separation o pupil samples where the waveront inormation can be measured independently. λ λ δ pupil = = = λ T T Which shows that the minimum distance between pupil measurements is the one o the sensor times the ratio o the ocals (microlens/telescope). Finally, i the condition o the plenoptic camera or best use o the detector is used [5] (Basically means that pupil images equal the microlens pitch) it can be directly deduced that the separation between pupil measurements is: T = (8) T µ L (7) δ pupil = (9) T which is exactly the same amount provided by the waveront sensor, because the ratio / T is the inverse o the number o subpupils in a telescope diameter, and is multiplying the microlens diameter, which represents the size o the pupil image.

6 4. LABORATORY PUPIL WAVEFRONT RECOVERY In order to veriy experimentally the capability o the plenoptic camera or acting as a waveront sensor, the optical setup described in ig 5 was built. The underlying idea was to have a method or varying the pupil waveront under user control, and then veriy up to what point the plenoptic sensor was capable o extract the generated waveront. A deormable mirror re-imaged on the aperture was used or that purpose. Object (solar granulation) Adjustable aperture Pulnix camera TM6740 e. Mirror 37 act Piezo (OKO) L1 =600mm L2 =120mm L3 =200mm Microlens Pitch: 400 µm = 25mm Fig. 5. Optical setup used or veriying the pupil plane waveront recovery by the plenoptic waveront sensor. Plenoptic camera is built using a 200 mm ocal length doublet (L3) plus the microlens array. An extended object simulating solar granulation (or any other with high spatial requency content) is collimated by L1 and L2 to be imaged by the plenoptic camera. At the same time the pair L1+L2 reimages the deormable mirror surace at the entrance pupil, allowing or direct control o the phase at this point. The plenoptic camera was built by combining a 200 mm ocal length acromatic doublet (L3) with a microlens array rom Adaptive Optics Associated, with 400 micron pitch and 25 mm ocal length. An adjustable aperture was used to reduce the aperture to the required value in order to have reasonable matched -numbers (3 mm aprox). The iris was located very close to the lens surace, practically glued to it. The plenoptic image was captured by a ast CC gig-e camera (Pulnix TM6740), having 640x480 squared pixels o 7.4 microns. Plenoptic images captured with this optical setup contain 10x8 pupil images, as shown in ig. 6. A number o objects were collimated to be imaged by the plenoptic camera, going rom a very simple cross to a solar granulation photograph, and also a blank reerence or lat ielding and microlens centres computation. Collimation is obtained using L1 ( = 600 mm) and L2 ( = 120mm) which also create a reduced image o the deormable mirror (25 mm, 37 piezo actuators rom OKOTECH) on the aperture, which provides phase control at this point.

all pupil coordinates. Fig. 7 depicts plenoptic images o a very simple object, a cross, viewed through the optical setup with two dierent positions o the deormable mirror.

It should be noted that the intermediate value in all actuators does not mean a lat mirror shape, due to residual latness error during mirror manuacturing. Fig. 7.

7 Fig. 6. Images showing the lat blank image o all pupils (let) and the result o reducing the aperture to its physical minimum to ind the position o the centers o the microlenses, which will be the reerence or all pupil coordinates. Fig. 7 depicts plenoptic images o a very simple object, a cross, viewed through the optical setup with two dierent positions o the deormable mirror. All actuators were set at the intermediate value, and actuator #14 was changed rom minimum actuation to maximum stroke. It should be noted that the intermediate value in all actuators does not mean a lat mirror shape, due to residual latness error during mirror manuacturing. Fig. 7. Plenoptic images o a cross at two dierent positions o actuator #14. Note that pupil images are not uniormly illuminated due to the inite distance to the object. The plenoptic images o ig 7 are recomposed in ig 8, ollowing the proposed scheme. A circular pupil is ound in both cases, and when both images are compared with some detail, it can be noticed that the movement o the cross depends on the pupil position sampled, with almost no change nearby the border and maximum towards the center o the pupil, where the actuator is located. This change is much more obvious when a movie o the movement o actuator #14 is recorded and played back. Correlation computation would ollow, but it will not add any more insight to the visual procedure and will not be included in this article.

8 Fig. 8. Recomposed pupil images o a cross, grabbed at two dierent positions o actuator #14. Note that maximum object displacement is ound at the center o the pupil, and its direction and magnitude vary according to the pupil coordinate being sampled. 5. COMPARISON WITH OTHER WAVEFRONT SENSORS Plenoptic waveront sensor could be considered as a generalization o the pyramid waveront sensor, in the sense that images o the pupil are used or computing the waveront, but without any moving part and to be used with extended or constellations o objects. The direct comparison should be with respect to the Wide Field Shack Hartmann waveront sensor also used or solar adaptive optics, where tomography is computed ater examining several zones o a wide ield o view on each subpupil. The main advantage is the absence o ield stop and pupil reimage, simpliying the optics needed. Also the capability o synthesizing virtually any aperture to work with allows adapting the adaptive optics system to dierent levels o turbulence, by changing even in real time- the order o the system in accordance with those levels. The price to be paid is the extra blurring induced on the pupil plane waveront estimation by the inite microlens diameter, and o course the extra processing needed. However, a very interesting capability o the plenoptic camera comes rom the possibility o obtaining images ocused to any height (or distance) by properly selecting the adequate pixels rom the microlenses images. This is a very powerul tool to be urther investigated in relation with the atmospheric turbulence tomography computation. 6. CONCLUSIONS, ACKNOWLEGEMENTS AN FUTURE WORK The plenoptic waveront sensor has been introduced and described, together with the analysis o its applicability to solar adaptive optics. espite its simplicity, it can be used or pupil plane waveront measurement to obtain the same resolution than the Shack-Harmann sensor, with the extra blurring caused by the inite (and normally small) size o the microlenses. Using a direct laboratory measurement, it has been shown that pupil plane waveront can be measured by the plenoptic camera. Future work includes the installation o a plenoptic camera at the VTT telescope, (Observatorio del Teide, Canary Islands, Spain) expected by summer A 2048 x 2048 pixel camera will be used or this purpose, with appropriate sampling o 10x10 pixels per pupil image. Real-time processing o the plenoptic sensor or solar images is also being developed, and a conceptual has already been presented at the AO4ELT Congress held in Paris last June. This work has been partially unded by the Spanish Programa Nacional I++i (Project PI ) o the Ministerio de Educación y Ciencia, and also by the European Regional evelopment Fund (ERF).

9 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] Ng, R., Fourier Slice Photography, Stanord University, (2005). Lippmann,M. G., Épreuves réversibles donnant la sensation du relie, J. de Phys. 4,VII,(1908). Lippmann, G., La photographie intégrale. Comptes-Rendus, Académie des Sciences 146, (1908). Adelson, T., and Wang, J. Y. A., Single lens stereo with a plenoptic camera, IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 2(Feb), , (1992). Ng, R. et al, Light ield photography with a hand-held plenoptic camera, Tech. Rep. CSTR , Stanord Computer Science, (2005). Georgiev, T., Lumsdaine, A., Superresolution with Plenoptic Camera 2.0, Adobe Tech Report, April (2009) Rodríguez-Ramos, J. M. International Patents ES ES (2006) Richard M. Clare and Richard G. Lane, "Wave-ront sensing rom subdivision o the ocal plane with a lenslet array," J. Opt. Soc. Am. A 22, (2005) Goodman, J.W., Introduction to Fourier Optics, 2nd Edition, McGraw-Hill, (1996)

The CAFADIS camera: a new tomographic wavefront sensor for Adaptive Optics.

1st AO4ELT conference, 05011 (2010) DOI:10.1051/ao4elt/201005011 Owned by the authors, published by EDP Sciences, 2010 The CAFADIS camera: a new tomographic wavefront sensor for Adaptive Optics. J.M. Rodríguez-Ramos