design of an interferometric system for the measurement of phasing errors in segmented mirrors

Design of an interferometric system for themeasurement of phasing errors in segmented mirrors

Carles Pizarro, Josep Arasa, Ferran Laguarta, Nuria Tomas, and Agustı Pinto

One of the new problems that has to be solved for segmented mirrors is related to periodic phasing,because for such mirrors to exhibit diffraction-limited performance the segments have to be positionedwith an accuracy of a fraction of a wavelength. We describe the optical design of an instrument thatmeasures the phasing errors �i.e., tip, tilt, and piston� between two segments under daylight conditions.Its design is based on a high-aperture white-light Michelson interferometer. It was developed at theCenter for Sensors, Instruments and Systems Development �CD6� of the Technical University of Cata-lunya, Spain, and its final testing was carried out on the Gran Telescopio Canarias test workbench.© 2002 Optical Society of America

OCIS codes: 110.6770, 350.1260, 120.3180, 120.3930, 120.4570.

1. Introduction

In the early 1980s the astronomical community dis-cussed the design of the next generation of telescopes,a generation that is now operative. The main issuethat had to be resolved was the design and construc-tion of a larger primary mirror. Scaling up themonolithic technology was not practical or affordable.Instead, the use of segmented mirrors, where manyindividual mirrors �the segments� work together toprovide an image quality and an aperture equivalentto those of a large monolithic mirror, was considereda more appropriate strategy. However, for a seg-mented mirror to provide good optical performance, aphasing process is required in order to guarantee thateach individual segment is properly positioned. Fornormal observing a positioning accuracy of tens ofnanometers is needed,1 but, when adaptive optics in-struments are to be used, this accuracy has to beimproved to a few nanometers.

The process of phasing a segmented mirror consistsof determining the positioning errors between neigh-boring segments, which may be caused by relativerotations and displacements of the segments, and

The authors are with the Center for Sensors, Instruments andSystems Development �CD6�, Technical University of Catalunya,Rambla Sant Nebridi, 10 E-08222 Terrassa, Spain. C. Pizarro’se-mail address is [email protected].

Received 7 January 2002; revised manuscript received 18 March2002.

0003-6935�02�224562-09$15.00�0© 2002 Optical Society of America

4562 APPLIED OPTICS � Vol. 41, No. 22 � 1 August 2002

then removing the errors by using a set of actuatorslocated under each segment. Once the initial mis-alignment has been removed, an active control sys-tem keeps the segments in their given initialpositions. Figure 1�a� shows two contiguous seg-ments and the reference system used hereafter, withthe Z axis oriented in the intersegment direction. Inthis reference system the possible positioning errorsof the segments are their relative rotations about theX axis ��X, or tilt� and the Z axis ��Z, or tip� and theirrelative vertical displacement along the Y axis �thepiston error; see Fig. 1�c��.

The effects of the positioning errors mentionedabove on the image of a distant star are substantiallydifferent, depending on whether these are rotationalor vertical displacement errors. Relative rotationsof the segments lead to relative displacements of theimages of the distant source created by each individ-ual segment. However, piston errors are displace-ments along the direction perpendicular to thesegments �Fig. 1�c��; they do not cause such displace-ments of the individual images but merely introducea phase difference between the images of the sourcefrom each segment �leading to incoherent segmentimaging�.

In addition, piston measurements need to be madewhen relative rotations �X and �Z have been correctedto such an extent that they are not detectable by thepiston measurement system. Otherwise, the pistonerror is not well defined, as it varies along the inter-segment �Fig. 1�b��. Obviously, because of the high-quality surface of the segments, noncontact opticalmeasurement techniques are required for measure-

ment of the initial misalignment. Whereas the con-trol of tip–tilt for such mirrors has beendemonstrated, absolute phasing �or piston control�presents a major challenge.2 Various optical tech-niques have been proposed in the literature,3,4 andthey can be classified as follows: diffractivetechniques,1,5–8 curvature sensing techniques,9–11 in-terferometric techniques,12–15 and phase diversitytechniques.16–19 Diffractive techniques analyze thediffraction pattern produced by the intersegmentalregion in which the piston phasing error is to bedetermined. Curvature sensing techniques recon-struct the wave front from a pair of defocused imagesof a star imaged by the segmented mirror, oneslightly inside and the other slightly outside focus.Interferometric techniques measure the piston errorby analyzing the interference pattern produced eitherin a plane conjugated to the segmented mirror orlocally at the intersegment zone. Phase diversity

techniques use an iterative technique to find the pu-pil aberrations that best match the measured dataobtained from a focused and a slightly defocused im-age.

Currently, only two segmented mirror telescopesare operative �the W. M. Keck telescopes�, and someothers are being built or designed �the Gran Telesco-pio Canarias �GTC� and the Telescopio InfrarojoMexicano �TIM��. The diffractive technique used inthe Keck telescopes is based on a physical optics gen-eralization of the Shack–Hartmann test. This tech-nique has a repeatability of the order of 10 nm,1,5 butit has the drawbacks that it uses starlight, as do mostof the devices proposed for use as phasing systems,with the consequent loss of astronomical observa-tional time, and that reducing piston errors from tensof micrometers to tens of nanometers requires aniterative technique �because of the small dynamicrange of each iteration�.

As was stated in GTC Conceptual Design20: “Atechnique should be implemented which allows thephasing of primary mirror segments without star-light so that it could be carried out during daytimewithout affecting the availability of observing time.This measurement can be carried out using an in-strument which detects the discontinuities of the pri-mary mirror in local intersegment zones.” Theinstrument that is described in this paper was devel-oped mainly to satisfy this requirement as well asothers found in GTC Conceptual Design20: The tech-nique should not require interaction with the tele-scope �e.g., stepping of the segments� and theaccuracy in piston measurement should be betterthan 5 nm �needed when adaptive optics systems areused�.

The paper is structured as follows: in Sections 2and 3 the main decisions concerning the methodologyand optical layout of the instrument are presented.Next, in Section 4, an optical analysis of the system isperformed, showing that the proposed layout permitsinterferometric piston measurements to be made dur-ing daytime. In Section 5 there is some discussion ofexperimental results obtained in the laboratory thatshow the feasibility of the proposed instrument. Fi-nally, in Section 6 our general conclusions are pre-sented.

2. Methodology

As we said above, the work of designing a phasingsystem grew from the general requirements that canbe found in GTC Conceptual Design.20 We proposeto use an interferometric technique to measure pistonphasing errors, as these provide the nanometric ac-curacy that the measurement requires. Moreover,the main advantage of interferometric techniques isthat they do not require using part of the telescope’sobservation time. Interferometers are able to oper-ate during daytime—they may use their own internallight sources—yielding a daily increment in the ef-fective observation time of the telescope comparedwith other phasing techniques.

The design of the phasing instrument, called UPC-

Fig. 1. �a� Reference system: the Y axis is defined along thedirection locally perpendicular to the intersegment, and the Z axisis oriented along the direction of the intersegment. �b� Relativeangular misalignment. �c� Relative vertical misalignment �pis-ton�. �b�, �c� Images extracted from the GTC web site �http:��www.gtc.iac.es�.

1 August 2002 � Vol. 41, No. 22 � APPLIED OPTICS 4563

ZEBRA, is based on the well-known amplitude divi-sion Michelson interferometer. This kind ofinterferometer was chosen in preference to otherssuch as the Mach–Zehnder15 and the lateral-shift12

interferometers because of its simple and versatileconfiguration and because it is able to fulfill the gen-eral requirements of a phasing instrument with fewmodifications.

To obtain the desired piston measurements weproject the measurement beam of the interferometer�Fig. 2� onto the intersegmental region in a directionthat is locally perpendicular to the segments, whichwas previously defined as the Y axis. This measure-ment beam is projected such that it evenly illumi-nates both segments. The reference beam of theinterferometer is projected entirely onto one of thesegments in a region situated as close as possible tothe intersegment. It is also projected in the direc-tion locally perpendicular to the segment at the pro-jection point.

The presence of pistons between segments will leadto a phase step in the wave front reflected from themeasurement region that will cause a fringe mis-match in the interference pattern, allowing the valueof the piston to be measured. Each full fringe dis-placement is interpreted as a ��2 piston phasing er-ror. However, if only monochromatic light wereused, piston phasing errors of multiples of ��2 wouldyield identical fringe shifts, and absolute piston val-ues could not be measured. To measure absolutevalues we also use white-light illumination in theinstrument. Once the piston between a pair of seg-ments has been measured, a robotic arm will positionthe interferometer on another intersegment and themeasurement procedure will be repeated until all theintersegments have been measured.

3. Optical Layout

The starting point of the design is the Twyman–Green variation of the classic Michelson interferom-eter layout, depicted in Fig. 3. A beam-splitter cube�BSC� divides the light from a collimated source intothe measurement and reference beams. Once the

two beams are projected onto the intersegment region�measurement beam� and the region of one of thesegments is used for reference �reference beam� thebeams follow their paths backward and, after beingrecombined by the beam splitter, interfere on theCCD array placed at the end of the observation armof the interferometer, which is in a plane that isconjugate to the segments. Using a region of one ofthe segments as a reference mirror has several ad-vantages compared with the classic Twyman–Greenoptical test setup: It provides a high degree of bothvibration insensitivity �as the same vibrations occurfor both measurement and reference beams� andwhat is called wave-front matching, which meansthat, even though the primary mirror is a hyperboloidwith typical values for the radius of curvature �R �33 mm� and for the conicity �k � �1.002250�, theinterference pattern, given the geometry of the UPC-ZEBRA interferometer, will not vary significantly,regardless of the intersegmental region under anal-ysis.

For mechanical reasons, however, the interferom-eter was built to work with its illumination and ob-servation arms in a plane parallel to the segments.In this plane the illumination arm is rotated 45° withrespect to the X axis and the observation arm is ro-tated 45° with respect to the Z axis, as depicted inFig. 4. To guide the measurement and referencebeams to the segments we place a pair of folding flatmirrors tilted at 45° �M2 and M3, Fig. 4� in both arms.As measuring the piston requires a number of fringesin the interferogram, mirror M3 is mounted upon arotation stage, MP3, which allows the fringe period tobe adjusted to the value required for the desiredpiston-error measurement range.

Fig. 2. The interferometric instrument: RB, reference beam;MB, measurement beam.

Fig. 3. Twyman–Green variation of the classic Michelson inter-ferometer layout: FD3, D3 focal object point; FD4, D4 focal imagepoint; D3, D4, doublets; BSC, beam-splitter cube.


One consideration in the optical design of the in-terferometer is the simultaneous use of both mono-chromatic and white-light sources. Doing this willenforce a full geometrical symmetry between themeasurement and reference arms of the interferom-eter, as no compensating plates can be used becauseof their high chromatic aberration.

An additional mirror, M1, is placed in the measure-ment beam path to desensitize the interferometer fromsmall relative rotation positioning errors of the inter-ferometer in the plane parallel to the segments ��X�.In addition, to ensure full geometrical symmetry be-tween the reference and measurement arms of theinterferometer, a linear displacement stage is placedbelow mirror M1 such that the optical path differencebetween the reference and the measurement wavefronts can be set to zero during system alignment.

Another modification of the Twyman–Green layoutis the introduction of an afocal imaging system in theobservation arm. This system permits imaging ofthe segments in the CCD array while simultaneouslyreducing the size of the incoming wave front to matchthe CCD array size. Thus the simultaneous obser-vation of the interference pattern and an image of thesegments allows a direct phase assignment to bemade to each point of the segments. Imaging thesegments is also useful for aligning and positioningthe interferometer. The observation arm was de-signed to be afocal to provide constant lateral mag-nification regardless of the working distance betweenthe interferometer and the segmented mirror. Fig-ure 5 shows schematically the final optical layout ofthe interferometer, including the afocal system justdescribed. As we explained in Section 2, piston errorvalues, measured when the relative angular mis-alignment between contiguous segments has been re-moved, will be extracted from the fringe mismatch inthe interferogram.

4. Design Analysis

Because the white-light interferograms will be usedonly to remove the ��2 indeterminacy of a monochro-

matic interferogram, a detailed analysis of the white-light interferometric system is not required.However, as the nanometric accuracy of the measure-ment system relies on monochromatic interfero-grams, a detailed analysis of the optical performanceunder monochromatic illumination is carried out.The first issue to consider is the extension of the lightsource used, as it must ensure a sufficiently flat wavefront before it strikes the beam-splitter cube. Next,an analysis of the quality of the measurement andreference wavefronts is made to ensure that thefringe mismatch in the interferogram is caused onlyby the piston between contiguous segments. Thisstudy is carried out under the assumption that theoptical path difference between the reference and themeasuring wave fronts has been completely compen-sated for and that relative rotations of the segmentsare so small as to be undetectable by the interferom-eter. Finally, the effect on the interfering wavefront of the afocal imaging system is studied andanalyzed to ensure that the interferogram remainsunaltered.

The illumination arm contains a collimating sys-tem, which consists of an achromatic doublet �Fig. 5,D3� with f-number N � 5.6 and diameter 63.5 mm,with the light source placed in the object focal planeof the doublet. Such a large aperture is necessaryfor this component and for some others because alarge observation area is needed to minimize the ef-fect on measurement accuracy of segment polishing

Fig. 4. Three-dimensional optical layout of the interferometer�the segments are not to scale�. M1–M3, mirrors; D3–D5, doublets.

Fig. 5. Insertion of an afocal system into observation arms �D4and D5� to image the intersegmental region on the detector planecombined with the interferogram fringes: FD3, D3 focal objectpoint, FD4, D4 focal image point; FD5, D5 focal object point; D3 toD5, doublets; BSC, beam-splitter cube.


errors, which are expected to be higher close to thesegment edges. The light source for the interferom-eter is an optical fiber coming from an external illu-mination system. The system contains a halogenlamp and a set of filters to select white light or mono-chromatic illumination. We obtain the monochro-matic source by inserting a bandpass interferentialfilter centered at 632.8 nm with a FWHM of 10 nm.To obtain the same illumination level on the CCDarray when white light is used, we insert a 2 OD�optical-density� neutral-density filter. The lightsource will have the size of the core of the optical fiberused, which has a diameter of 600 m. The firstthing that has to be done is to evaluate the effect ofthis extension on the collimation quality of the wavefront leaving collimator D3. The optical path mapsof the collimated wave front leaving D3 on-axis �Fig.6�a�� and at the edge of the source �d � 300 m; Fig.6�b�� are presented as contour plots with a contourstep height of ��100; the central wavelength of theinterference filter �632.8 nm� is used. We calculatedthe values at the edge of the source by subtracting thepath difference caused by the wave-front tilt associ-ated with a light source placed off-axis �the paraxialcomponent hereafter�. This component does notplay an important role in the interferogram, as eachpoint in the incident wave front is interfering withitself, and the phase differences in the two arms arethose that lead to the final intensity value.

The results in Fig. 6 show how, for a source placedon-axis, the wave-front departure from a perfectlycollimated wave front remains less than 5��100.The maximum divergence value in the collimatedbeam is less than 1.7 � 10�3 rad. The results for apoint source placed at the edge of the field are equiv-alent, once the paraxial component has been sub-tracted. This deviation from the perfect beam iswell within the collimation requirements for a wavefront striking the beam-splitter cube to produce in-terferograms that allow nanometric distance mea-surements. This means that the wave front at theoutput of the imaging system is no longer required tobe flat; any wave front is valid as long as the imagingsystem does not overlap different wave fronts comingfrom different points of the light source. If it did, aloss of contrast would be observed. The equivalenceof behavior of an on-axis and a field point sourceguarantees good interferogram quality �contrast�.The wave-front asymmetry that can be seen in Fig. 6is due to small positioning errors of optical elements,because for this instrument the mechanical position-ing precision is 1 m. This asymmetry is alsopresent in other wave fronts �Figs. 7–9�, but it isobservable only in Figs. 6 and 9. As we shall see, thisasymmetry will have no effect on measurement ac-curacy.

Next, the effect of the beam-splitter cube on wave-front quality is analyzed. To isolate the optical ef-fects of the beam-splitter cube we have assumedreflection onto perfect segments precisely aligned inthe absence of relative rotation and piston errors. Ithas also been assumed that the beam splitter is per-

fect and has a transmission�reflection ratio of 50:50.The beam splitter’s effect on wave-front quality willagain be different for an on-axis source and for a fieldsource. Figure 7 shows a plot equivalent to that ofFig. 6 but after the wave fronts have crossed thebeam-splitter cube twice. The contour step curves ofthe optical path differences are again plotted with acontour step height of ��100. Again, the on-axissource yields departures from the perfectly flat wavefront of less than ��20 �Fig. 7�a��, whereas the fieldsource �Fig. 7�b�� yields an equivalent wave front withdepartures from the perfectly collimated beam alsoremaining less than ��20 once the paraxial compo-nent of the wave front is removed. It should benoted that the wave front is not degraded after itcrosses the beam splitter twice, as the degree of de-

Fig. 6. Optical path maps after the wave front leaves the D3collimator, presented as contour plots: �a� point light source onaxis, �b� point light source placed at the edge of the object field ofthe collimator �300 m� when the paraxial component has beensubtracted �� 632.8 nm; contour step ��100�.


parture from the flat wave front is the same as it wasbefore the wave front crossed the cube.

The last step in our analysis considers the effect onthe interferograms of the afocal system introduced inthe observation arm to image the intersegmental re-gion at the same time as the interference pattern.The equivalence of the wave fronts obtained from apoint source placed on-axis and at the edge of thesource should still be observed in the wave fronts thatare leaving the afocal system. These wave frontswill no longer be flat, but, to permit adequate inter-ferogram fringe observation, the afocal imaging sys-tem should not introduce phase differences betweenthe on-axis and the edge-of-field wave fronts.

The detector is a 768 by 576 pixel CCD array placedin a plane conjugated to the segments of the afocalsystem with a lateral magnification of m � 0.14 de-

termined by the required object and image sizes.The system works with a maximum field of view of1.7 � 10�3 rad owing to the finite extension of thelight source and permits the simultaneous imaging ofthe intersegment region with a field of view of 45.3mm by 34 mm, enough for our piston measurementpurposes, and the interference pattern.

Following the optical path difference plots in Figs.6 and 7, Fig. 8 depicts the optical path differencesfrom an axial light source �Fig. 8�a�� and a pointsource placed at the edge of the field �Fig. 8�b�� withthe paraxial component removed, after the lightpasses through the afocal imaging system placed inthe observation arm. To achieve a good-quality im-aging system combined with interferogram fringe ob-servation, we allow the afocal system to change theconvergence of the incoming wave front �a 4� opticalpath difference variation may be observed in the

Fig. 7. Optical path maps after the wave front leaves the beam-splitter cube, presented as contour plots: �a� point light source onaxis; �b� point light source placed at the edge of the finite extent ofthe source �300 m� when the paraxial component is subtracted�� 632.8 nm; contour step ��100�.

Fig. 8. Optical path maps after the wave front crosses crossingthe afocal imaging system, presented as contour plots: �a� pointlight source on axis, �b� point light source placed at the edge of thefinite extent of the source �300 m� when the paraxial componenthas been subtracted �� 632.8 nm; contour step ��10�. Note theequivalence of the two plots, which ensures that the afocal systemdoes not distort the interferograms that are recorded.


wave front�, although the system does not introducephase changes in addition to those that are present inthe incident wave front. This means that the wavefront leaving the optical system is no longer flat, al-though it keeps a constant shape for all possiblesource field values. These features may be appreci-ated from Fig. 8 for sources on the axis and at theedge-of-field values. To verify that this behavior iscorrect we calculated the differences in the wavefronts plotted in Fig. 8 at a set of points along theirtangential and sagittal sections; the deviations havebeen plotted in Fig. 9. Wave-front deviations ob-tained from the edge-of-field point source relative tothe on-axis source may be seen always to be less thanthe ��50 value, which ensures that the interferogramfringes will not be noticeably affected by the aberra-tions introduced by the afocal system. As in Fig. 6,the asymmetry that can be observed in this figure isdue to small positioning errors of optical elements,because for this instrument the mechanical position-ing precision is 1 m. This analysis allows us tostate that interference fringe mismatching will becaused only by errors in the relative positioning of thepair of contiguous segments under analysis. FromFigs. 6–8 the optical quality of the optics to be usedcan also be extracted: ��20 optical quality isneeded.

5. Results

We used the layout described above to build an in-terferometric piston-phasing-error measurement in-strument. The interferometer was designed andbuilt at the Center for Sensors, Instrumentation andSystems Development of the Technical University ofCatalunya and tested at the Gran Telescopio Canar-ias test workbench.

As expected, the imaging system permits a clear

vision of the area being tested, which is made fromthree clearly separated regions �Figure 10�a��, namely,the upper subfield, where the reference wave front�from segment 2� interferes with the half of the mea-suring wave front that comes from segment 1; the in-tersegment area; and the lower subfield, where thereference wave front interferes with the half of themeasuring wave front that comes from the same seg-ment �segment 2�. The presence of a piston will leadto fringe mismatching in the interference pattern,which will become evident when white-light illumina-tion is used �see Fig. 11�b��. Residual tip and tilt an-gular misalignment will also have an effect on theupper subfield fringe pattern, allowing it to be ex-tracted as well: Relative tilt between segments willcause the fringe period to change, and relative tip willcause the fringes to deviate from the vertical.

Figures 10 and 11 show representative interfero-grams registered on the CCD array and used forpiston-error determination. The piston measure-ment range was set to 12 m, but the actual piston ineach figure is different: in Fig. 10 the piston is zeroand in Fig. 11 the piston is close to 8 m. Figures10�a� and 11�a� show a monochromatic interfero-gram; whereas Figs. 10�b� and 11�b� are white-lightinterferograms. Note how the ��2 indeterminacythat is intrinsic in monochromatic interferograms iseasily removed by use of white-light illumination. Itis also interesting to note that the number of observedfringes in the interferograms can be adjusted by useof rotation axis MP3 on mirror M3 to obtain the de-sired value for the piston measurement range, whichis limited only by the fringe sampling at the CCDarray. Laboratory tests have shown that the system

Fig. 9. Deviations along the tangential and sagittal sections ofthe wave fronts depicted in Fig. 8, corresponding to an on-axis andan edge-of-field point light source. The maximum deviation re-mains less than ��50. Fig. 10. Real interferograms obtained with the instrument that

we have designed in a piston-phasing-error measurement range of12 m. The actual piston is 0 m �phased segments�: interfero-grams obtained with �a� monochromatic light �� 632.8 nm� and�b� white light.


is able to measure a piston range of 12 m betweensegments with a repeatability of 5 nm rms as well asresidual tip and tilt misalignments. A picture of thephasing instrument is shown in Fig. 12. Additionalfolding mirrors, M4 and M5, were placed in the illu-mination and observation arms, respectively, to re-duce the dimensions of the instrument. Also, M1was provided a displacement positioner �MP1� foroptical path difference balancing. The system’s per-formance has also been tested on the GTC test benchunder workshop conditions.

6. Conclusion

The interferometric piston-phasing-error measure-ment system presented here has the desirable prop-erty of being able to carry out the phasing of asegmented mirror during daytime, saving valuableobservation time for scientific purposes. Moreover,the dynamic range has been increased with respect tothose of other phasing techniques that have beenproposed, e.g., the one used at the Keck telescopes.We propose mounting the interferometer upon a ro-botic arm and measuring the piston phasing errorlocally at each intersegment. This procedure hasthe advantages that the primary segmented mirror ofa telescope can be phased during daytime while thetelescope is pointing at the expected observation re-gion of the sky and thus will suffer no gravitationalstresses and also that the segmented mirror can bephased again less than 10 min a segment after beingexchanged.

An optical design of an interferometer for the localmeasurement of piston-phasing errors in segmentedmirrors has been described. Starting with a classicMichelson interferometer layout, a set of modifica-tions was introduced to make it suitable for use as aphasing instrument. Folding mirrors are used toguide the beams along the required direction suchthat the reference beam of the interferometer falls onone of the segments, and the measurement beam isequally divided between the two contiguous segmentswhose misalignment is to be measured. An afocalimaging system placed in the observation arm per-mits imaging of the intersegmental region withoutdistorting the interferograms. Piston-error mea-surements will be obtained from the fringe mismatchin the interferogram. Both monochromatic andwhite-light interferograms will be obtained to solvethe ��2 indeterminacy. A detailed analysis of thewave-front quality as it travels along the various op-tical elements of the interferometer has been per-formed, showing the validity of the proposedinterferometer design. Finally, some results ob-tained at the test workbench and in the lab have beenshown, which provide consistent proof of the capabil-ity of the proposed instrument to determine accu-rately the piston phasing error in segmented mirrorsduring daytime, with the required nanometric re-peatability. Lab tests have also shown that the sys-tem is able to measure residual tip and tiltmisalignments.

Fig. 11. Real interferograms obtained with the instrument thatwe have designed in a piston-phasing-error measurement rangeof 12 m. The actual piston is �8 m. Interferograms ob-tained with �a� monochromatic light �� 632.8 nm� and �b� whitelight.

Fig. 12. Picture of the phasing instrument in the laboratory:OF, optical filter; OFP, optical filter positioner; M1–M5, mirrors;MP1, MP3, mirror positions; BSC, beam-splitter cube; D3–D5,doublets.


This study was financed by the Comision Intermin-isterial de cienca y Tecnologıa �Spain� through thePrograma Nacional de Tecnologıas Avanzadas de laProduccion �TAP96-1043�, and by GRANTECAN S.A.A. Pinto thanks the Departament d’Universitats, Re-cerca i Societat de la Informacio �Catalunya regionalgovernment�, for the PhD grant he received, whichpermitted him to take part in this research.

References1. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T.

Mast, and D. Kirkman, “Phasing the mirror segments of theKeck telescopes: the broadband phasing algorithm,” Appl.Opt. 37, 140–155 �1998�.

2. G. Chanan, J. Nelson T. Mast, P. L. Wizinowich, and B.Schaefer, “W. M. Keck Telescope phasing camera system,” inInstrumentation in Astronomy VIII, D. L. Crawford and E. R.Craine, eds., Proc. SPIE 2198, 1139–1150 �1994�.

3. M. Owner-Petersen and T. Andersen, “Overview of optical me-trology for segment phasing,” in Workshop on Extremely LargeTelescopes �E. Jurlander, Lund, Sweden, 1999�, pp. 152–161.

4. A. Schumaker, L. Montoya, N. Devaney, K. Dohlen, and P.Dierickx, “Phasing ELT’s for adaptive optics: preliminary re-sults of a comparison of techniques,” presented at the BeyondConventional Adaptive Optics Conference, Venice, Italy, 7–10May 2001.

5. G. Chanan, C. Ohara, and M. Troy, “Phasing the mirror seg-ments of the Keck telescopes II: the narrow-band phasingalgorithm,” Appl. Opt. 39, 4706–4714 �2000�.

6. A. Weitheimer and T. Dey, “Wide-range, high-accuracy, whitelight piston sensor for segmented optics,” Opt. Eng. 34, 2149–2156 �1995�.

7. J. T. Watson, “Experimental study of mirror segment phasingusing tungsten light,” Opt. Eng. 27, 758–761 �1988�.

8. N. C. Mehta and C. Allen, “Remote alignment of segmentedmirrors with far-field optimization,” Appl. Opt. 31, 6510–6518�1992�.

9. G. Chanan, M. Troy, and S. Sirko, “Phasing the Keck tele-scopes with out-of-focus images in the infrared,” Appl. Opt. 38,704–713 �1999�.

10. V. G. Orlov, S. Cuevas, F. Garfias, V. V. Voitsekhovich, andL. J. Sanchez, “Co-phasing of segmented mirror telescopeswith curvature sensing,” in Telescope Structures, Enclosures,Controls, Assembly�Integration�Validation, and Commission-

ing, T. A. Sebring and T. Andersen, eds., Proc. SPIE 4004,540–551 �2000�.

11. J. M. Rodriguez-Ramos and J. J. Fuensalida, “Phasing seg-mented mirrors: new algorithm and numerical results forpiston detection,” in Optical Design, Materials, Fabricationand Maintenance, P. Dierickx, ed., Proc. SPIE 4003, 270–278�2000�.

12. H. W. Klumpe, B. A. Lajza-Rooks, and J. D. Blum, “Absolutephasing of segmented mirrors using the polarization phasesensor,” Rev. Sci. Instrum. 63, 1698–1706 �1992�.

13. R. F. Horton, E. E. Huber, L. A. Bernotas, L. G. B. Yee, A. V.Roberts, J. M. Norton, E. G. Corbett, and R. A. Humphreys,“Absolute piston phasing of segmented-mirror optical systemsusing depth-modulated white-light interferometry,” in Ad-vanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc.SPIE 1236, 974–984 �1990�.

14. K. Dohlen, F. Decortiat, F. Fresneau, and P. Lanzoni, “Dual-wavelength random-phase-shift interferometer for phasinglarge segmented primaries,” in Advanced Technology Opti-cal�IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE 3352, 551–559 �1998�.

15. B. Jacobsen and R. Angel, “High accuracy wavefront stellarwavefront sensing using a Zernike interferometer,” Bull. Am.Astron. Soc. 26, 1373–1381 �1994�.

16. R. G. Paxman and J. R. Fienup, “Optical misalignment sensingand image reconstruction using phase diversity,” J. Opt. Soc.Am. A 5, 914–922 �1988�.

17. R. L. Kendrick, D. S. Acton, and A. L. Duncan, “Phase diversitywavefront sensor for imaging systems,” Appl. Opt. 33, 6533–6546 �1994�.

18. M. G. Lofdahl, R. L. Kendrick, A. Harwit, K. E. Mitvhell, A. L.Duncan, J. H. Seldin, R. G. Paxman, and D. S. Acton, “A phasediversity experiment to measure piston misalignment on thesegmented primary mirror of the Keck II telescope,” in SpaceTelescopes and Instruments V, P. Y. Bely and J. B. Breckin-ridge, eds., Proc. SPIE 3356, 1190–1201 �1998�.

19. S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y.Liu, and D. Cohen, “Performance of wavefront sensing andcontrol algorithms on a segmented telescope testbed,” in UV,Optical and IR Space Telescopes and Instruments, J. B. Breck-inridge and P. Jakobsen, eds., Proc. SPIE 4013, 749–756�2000�.

20. GTC Project Office, ed., GTC Conceptual Design �GrantecanS.A. 1997�, http:��www.jtc.iac.es.


design of an interferometric system for the measurement of phasing errors in segmented mirrors

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