Lightweight hollow rooftop mirrors forstabilized interferometry

Robert J. HillTrevor L. CourtneySamuel D. ParkDavid M. Jonas

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Lightweight hollow rooftop mirrors for stabilizedinterferometry

Robert J. HillUniversity of ColoradoDepartment of PhysicsBoulder, Colorado 80309-0390

Trevor L. CourtneySamuel D. ParkDavid M. JonasUniversity of ColoradoDepartment of Chemistry and BiochemistryBoulder, Colorado 80309-0215E-mail: david.jonas@colorado.edu.

Abstract. Hollow rooftop mirrors, also known as dihedral retroreflectors,can simultaneously preserve polarization, minimize chromatic dispersion,and allow beams to be stacked inside an interferometer. Two hollow roof-top mirrors were fabricated and characterized using a Fizeau interferom-eter and an inexpensive home-built jig instead of a master cube. The masswas 3.3 g for a clear aperture surface area of 110 mm2 with maximumretroreflected beam deviation of 12 arc s. With a hollow rooftop mirrormounted on a piezoelectric transducer in one arm of a Mach-Zehnderinterferometer, a displacement stability of �0.8 nm rms was achievedusing active feedback. The rooftop mirrors’ suitability for Fourier transformspectroscopy was demonstrated. © The Authors. Published by SPIE under a CreativeCommons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole orin part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.OE.52.10.105103]

Subject terms: retroreflector; hollow rooftop mirror; hollow roof mirror; actively sta-bilized interferometer; dihedral retroreflector; Porro mirror; hollow Porro prism.

Paper 130962 received Jun. 27, 2013; revised manuscript received Aug. 30, 2013;accepted for publication Sep. 13, 2013; published online Oct. 4, 2013.

1 IntroductionRetroreflectors have found many precision metrology uses,from measurements of distances1 and machining,2 to stabi-lized3 and scanning interferometers.4 The main advantage ofusing a retroreflector over a mirror is that it returns the lightto its source without great sensitivity to alignment.5 Whilethere are many retroreflector designs, hollow retroreflectorsserve an important role in Fourier transform spectroscopy,6

laser stabilization,7 and interference-based ultrafast tech-niques.3,4 Hollow retroreflectors are preferred over otherdesigns because they have lower masses than solid retrore-flectors. They also minimize the chromatic dispersion thatlengthens ultrafast pulses. For ultrafast spectroscopy, stabi-lization is often accomplished by 90 deg reflection froma single displacement-stabilized mirror, but this leads tophase shifts that are readily detectable with Fourier transformspectral interferometry.8 These phase shifts can be eliminatedby mounting retroreflectors on piezoelectric transducers.3

Hollow rooftop mirrors (HRMs) allow beams to bestacked without inversion of the stack and can preservepolarization (unlike trihedral retroreflectors). For a 90 degangle between plane mirror surfaces, HRMs retroreflectlight incident in planes perpendicular to the mirror jointaxis (dihedral retroreflection). The drawbacks to HRMsare that dihedral retroreflection is sensitive to the inclinationangle of the incident beam to the mirror joint axis,6 that thepolarization and stacking advantages are sensitive to rotationof the rooftop mirror in the plane of the aperture, and thatpreservation of s or p polarization is sensitive to the incli-nation angle.

A reflector’s mass limits the achievable bandwidth gov-erning displacement-stability in interferometers,9 providingmotivation to reduce retroreflector mass in order to achievegreater displacement-stability. The primary difficulty in con-structing hollow rooftop10 and trihedral11 retroreflectors canbe traced to the mechanical design joining the mirrors. Thischallenge becomes amplified when scaling down to smaller

and lighter retroreflectors that can have reduced contact areabetween mirrors, in contrast to difficulties encountered whenscaling up the size of prisms.12 References that discuss solidprism fabrication13 mention solid retroreflectors as mastercubes for hollow retroreflectors, but a detailed descriptionof hollow trihedral (corner cube) retroreflector fabrica-tion11,14 is rare; in particular, critical bonding materials areusually omitted as proprietary.10,15–17 One route involvesassembly of coated mirrors in a permanent support structurefollowed by measurement and adjustment while bonding andcuring;16,17 the other involves assembly and direct bonding ofuncoated mirrors on a master prism, followed by coating.10,11

The method presented here bonds coated mirrors directlywhile measuring and adjusting the dihedral angle, allowingfabrication of HRMs that are lighter and have a greater sur-face area to mass ratio than those commercially available.17

2 ExperimentalTwo HRMs were each constructed18 from a rectangular“enhanced silver broadband visible and infrared metal anddielectric mirror” with a λ∕10 front surface at 632 nm(JML MPS 14407/309—suffix 309 indicates coating withmetallic silver and a protective dielectric overcoat designedfor reflectance over 98% across the 500 to 1100 nmwavelength range and for cleaning with water, alcohol,and acetone;19 this coating has different specifications fromthe reflective coating with suffix 309 currently on the JMLweb site20). Mirror dimensions were 17.8 mm × 13.8 mm,with a 3.2 mm Pyrex® substrate thickness. The mirrorwas cut into two pieces with a low-speed diamond wheelsaw (South Bay Technology® Model 650, typically usedfor cutting semiconductor wafers), using a 3 in. diameter,0.006 in. thick blade. Letting a represent the thickness ofthe glass substrate, the total length (17.8 mm here) is cutinto two pieces with lengths L and Lþ a, making L ¼7.3 mm. This gives each HRM a maximum total projectedarea of 10.3 mm × 13.8 mm.

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A jig was constructed by bolting two kinematic mirrormounts (New Focus, 9809 Classic Corner Mirror Mounts)to the plane of a free standing aluminum block wall. Themirror mounts formed a 90 deg V angle with each mirrorat 45 deg angle with respect to the base of the block wall.The two mirror halves were placed in the V groove withtheir mirrored surfaces facing up, as shown in Fig. 1.

A Fizeau interferometer21,22 (Zygo, GPI-XP, using theMetropro software app for characterizing the surface heightof flats—the Metropro corner cube app was not available)characterizes the two-dimensional phase profile by sendingout a 632.8-nm wavelength helium neon laser plane wave toreflect off the HRMs and interfere with a reference planewave. In this single pass test,23 the reflected rays follow opti-cal paths from the reference plane down to the first mirror,across to the second mirror, and back up to the referenceplane. With respect to a reference, bright fringes representphase differences of 2nπ (integers n), while alternatingdark fringes represent phase differences of ð2nþ 1Þπ. Thewavefront difference (in waves) between two rays measuredwith a Fizeau interferometer equals the quotient of the opti-cal pathlength difference between those two rays dividedby the measuring wavelength (for a mirror, the optical path-length difference is exactly twice the surface height differ-ence). Asymmetrical wavefront errors introduced by theinterferometer will appear twice as severe as they reallyare in a single pass test, and all measured asymmetries acrossthe mirror joint axis in the returned wavefront arise from theinterferometer.23

To achieve the final result, mirror angles were aligned inthe jig three times while monitoring the interference fringes.The first alignment sets the jig up correctly with the mirrorssimply resting on it; this alignment step is necessary becausethe mirror of length Lþ a makes contact with both mirrormounts of the jig (see Fig. 1). A single fringe across theentire surface rendered the two mirrors nearly indistinguish-able from a flat mirror and was indicative of an ideal 90 degangle whose continuity was broken by a thin line where thetwo halves were joined. To set the approximate bondingangle and position, the mirror of length Lþ a was thenaffixed to one mirror mount with a layer of molten thermo-polymer (Crystalbond™ 509 washable adhesive, solublein acetone, flowpoint 121°C) less than ∼0.25 mm thick asjudged by eye. The shorter mirror was then slid into position

using the mirror mount as a guide ramp until the side cut withthe diamond saw rested on the reflective surface of the longermirror (Fig. 1). In preparation for bonding, a second align-ment restored a single fringe across both mirrors. Then,a thin (width ∼1 mm as judged by eye on the 3.2 mm thicksubstrate) bead of adhesive (Torr Seal®, Varian) was appliedto the cut side of the shorter mirror with a toothpick andit was slid back into position, bonding the two mirrors. Thethird alignment took place immediately after this applicationof adhesive to the joint between mirrors.

While the adhesive cured during the first two hours, smalland incremental adjustments were made to the dihedralangle. As the adhesive dried completely, smaller drifts, typ-ically much less than λ∕20 occurred over the following∼24 h. Heating the underside of the optical mount allowedremoval of the HRM from the thermopolymer adhesive with-out softening the Torr Seal® at the HRM joint.

Using Torr Seal® as the adhesive was crucial. A numberof bonding agents were attempted without success, includingcyanoacrylate24 (Duro Super Glue), UV curable epoxy adhe-sive (Epo-Tek OG116), two component thermally curedepoxy (Epo-Tek 353ND), two part epoxy (HardmanDouble/Bubble Extra Fast Setting Epoxy), and white glue(Elmer’s Glue-All). The common problem was that largechanges in the angle between mirrors occurred while curing.Two adhesives [Stycast 2850 with catalyst 9 (Emerson andCuming) was found to have lower thermal expansion thanEPON Resin 828 with curing agent Versamid 140] and atongue and groove assembly for minimizing such changeshave been discussed,11 as has hydroxide bonding of uncoatedsubstrates.14 Exploration of specialized bonding cements andadditives11,14,24,25 was inhibited by cost. Torr Seal®, on theother hand, has long been used for bonding Brewsterwindows26 and end mirrors in stabilized laser cavities, sug-gesting that angles can be set and that it forms a mechanicallystable bond compatible with an actively stabilized interfer-ometer element. The high Young’s modulus of Torr Seal®has proven useful in mounting tuning fork tips for atomicforce microscopy.27 Torr Seal® is a high vacuum adhesivewith a high specified28 shear strength of 13.8 MPa(2000 psi), a useful temperature range of −45 to 120°C, alow coefficient of thermal expansion of 30.3 × 10×6∕°C,and a high Young’s modulus [estimates from the specifiedShore D hardness of 75 to 80 range from ∼400 MPausing Fig. 11 of Ref. 29 to ∼9 GPa (Ref. 27)]; comparedto representative structural adhesives,25 all of these suggestTorr Seal® can be useful for mounting optics.

To prevent bending of the HRM, side supports (alsocalled end plates24 or end braces) were added. For lowmass, these reinforcements were constructed of glass micro-scope cover slips (VWR Micro Cover Glasses, #48366-205,18 mm × 18 mm × 0.18 mm) cut into a shape resembling aSuperman© shield (see Fig. 2) and attached with Torr Seal®.After pressing the support into place, the HRM was posi-tioned so that the support was on top of the HRM as theadhesive cured (Fig. 2). The adhesive for the first supportwas allowed to cure for 24 h before the second was attachedin the same manner and allowed to cure for 24 h. The aboveprocedure was adopted to minimize distortion from the over-constraint applied by the side supports. Measurements of theretroreflected wavefront at each step of the above processdiffer by <0.1 wave peak-to-valley. This overconstraint

Fig. 1 Mirror positioning on the jig. The coated mirror surfaces areuppermost (medium gray); the mirror sides cut with the diamondsaw are marked with diagonal hatching. The longer mirror was firmlyaffixed to the optics mount (on the right) by pressing it into a thin layerof molten thermopolymer adhesive (dotted light gray). To preventsmearing Torr Seal® on the longer mirror, the shorter mirror wasslid in the direction of the arrow along the optic mount into its bondingposition to form a 90 deg contact-angle with the longer mirror.

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distortion is present in the retroreflected wavefront analyzedbelow and is acceptable for the application demon-strated here.

Finally, the HRM was bonded into a V groove in a ½ in.diameter cylindrical aluminum base with a flat back surface(for attachment to the piezoelectric transducer). The flat backsurface of the base was mounted to the jig with double-sidedtape so that one face of the base’s V groove would remainhorizontal while the other remained vertical, see Fig. 3. Athin piece of paper set an air gap between the verticalside of the V groove and the smaller mirror. The largest mir-ror was pressed into Torr Seal® on the horizontal surface ofthe V groove so that only gravity applied pressure across theresting surface while it cured. When bonding the HRM to thealuminum base, the vertical air gap was necessary in order toprevent mechanical interference from misaligning the preci-sion of the bond angle as the Torr Seal® cured. Compared tomounting with adhesive on two surfaces of one mirrorelement,30 mounting a retroreflector using adhesive ononly one rear surface of one mirror element reduces stress;31

mounting the one rear surface directly to the metal base30

(rather than using an intermediate glass bonding surfacefor enhanced thermal stability31) reduces total mass andimproves mechanical stability. While cutting the aluminumbase at the reflective point of symmetry could reduce themass further, this was not done to minimize torques onthe piezoelectric transducer. After the Torr Seal® hadcured for 24 h, the HRMs were placed inside the Fizeauinterferometer for final analysis.

3 ResultsThe retroreflected wavefront from one HRM is shown inFig. 4. Like an ideal plane mirror, an ideal hollow rooftopwith a 90 deg mirror joining angle returns a wavefront

with a flat phase, so the quality of the HRM can be measuredwith the same surface figures using the Fizeau interferom-eter. The retroreflected wavefront is symmetrical underreflection across the mirror joint axis (a vertical line at X∼4.4 mm in Fig. 4); asymmetries on the order of 0.04waves arise from the interferometer. The first standard sur-face figure is the peak-to-valley wavefront distortion, whichmeasures the maximum retroreflected wavefront differencewith respect to a planar surface in units of the 632.8 nmmeasuring wavelength. The second standard surface figureis the rms wavefront distortion, which measures the rootmean square deviation (in waves) of the retroreflectedwavefront from a linear fit (the linear fit will remove anyretroreflected beam deviation). The first hollow rooftopretroreflector (total mass of 3.4 g for retroreflector andbase) had retroreflected wavefront distortions of 0.07waves rms and 0.38 waves peak-to-valley over 90% ofits 8.5 mm × 13.2 mm aperture. Figure 4 shows both theaperture (inside dashed lines) and the 90% usable area(inside boxes chosen to exclude edges and the joint) overwhich the wavefront distortions are calculated. The secondHRM (total mass 3.2 g) had 0.07 waves rms and 0.39 wavespeak-to-valley wavefront distortions over 90% of an8.9 mm × 13.8 mm aperture. The wavefront distortions areslightly less than expected from the mirror specifications.Assuming that symmetrical interferometer distortionshave the same magnitude as asymmetrical interferometer

Fig. 2 End brace for the roof mirror. (a) The side supports wereattached with a thin (∼1 mm) bead of Torr Seal®. (b) After the sidesupport was pressed firmly into place, the assembly was set withthe new side support facing up so as to dry under uniform, minimalpressure from its own weight.

Fig. 3 Mounting the hollow rooftop mirror in the aluminum base. Thehollow rooftop mirror was positioned in the base so that gravityexerted uniform pressure on the bond while it dried. Note drawingnot to scale.

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Fig. 4 Contour map of the retroreflected wavefront from the hollowrooftop mirror with 3.2 g mass. The retroreflector clear aperture isenclosed in dashed lines. The usable area is enclosed in two solidrectangles, which exclude the mirror edges and the vertical jointbetween mirrors and enclose 90% of the clear aperture area(8.9 mm × 13.8 mm). Within the usable area, wavefront contoursare indicated in bold grayscale, ranging from 0 to 0.36 waves ofthe red HeNe (632.8 nm) and labeled as on a topographic map.Outside the usable area, wavefront contours are indicated by uniformlight gray contours, with peaks at both vertical edges and a valley inthe joint between mirrors. Within the active area, the mean wavefrontis at 0.16 waves, the rms wavefront distortion is 0.07 waves, and thepeak to valley wavefront distortion is 0.39 waves.

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distortions suggests total measurement errors of 0.06 wavespeak-to-valley, which is consistent with the agreementbetween measurements at successive steps in fabricationand with the agreement between the two retroreflectors.

Independent of the angle of incidence within planesperpendicular to the mirror joint axis, a dihedral retroreflectormirror joining angle of ðπ∕2Þ þ α will return the incidentbeam at π þ 2α, so that the retroreflector beam deviation is2α. The maximum ratio of wavefront difference f to lateraldistance d determines the worst-case retroreflector beamdeviation, 2α ¼ arctanðfλ∕dÞ. For a simple error in joiningangle, the peak-to-valley wavefront difference occurs over adistance of half the clear aperture.5 With fp−v ¼ 0.38 waveand using half the clear aperture for the distance, dp−v ¼4.2 mm, the retroreflected beam deviation is 5.7 × 10−5 rad(12 s of arc). For the two HRMs, the actual peak-to-valleydistance is in one case greater than (and in the other caseequal to) half the clear aperture, so these estimates of retro-reflected beam deviation are conservative. Over a year afterfabrication, the rooftop mirror reflectance measured forp-polarized light at 632 nm wavelength was 95.4� 0.3%,close to that expected in a double pass from the specified98.3% reflectance of the mirror for unpolarized light.

These low-mass HRMs were used in both arms of a smallMach-Zehnder interferometer mounted on a breadboard ontop of a vibration isolated table; the interferometer was opento air. The beams entered the HRMs on one side and left onthe other,6 enclosing an area of ∼10 cm2. A piezoelectrictransducer was attached to the back of HRM to actively sta-bilize the interferometer displacement using feedback from apolarized continuous wave 632.8 nm wavelength HeNelaser.3,32 Acceleration of the retroreflector during active inter-ferometer stabilization with the piezoelectric transducer is upto ∼10−2 g (rms) in a 50 Hz to 3 kHz frequency range.Interferometer displacement was independently monitoredoutside of the feedback loop using a polarized continuouswave 594.1 nm wavelength HeNe laser.3 The yellow andred beams were copropagating; the HRMs allowed femtosec-ond laser beams to be stacked above them inside the inter-ferometer. A displacement stability of �0.8 nm rms wasmeasured over 0.1 Hz to 10 kHz, demonstrating the struc-tural rigidity of the HRM required for use in actively stabi-lizing an interferometer.

The retroreflected beam deviation determines the maxi-mum lateral movement of the beam center as the retroreflec-tor is translated. For a 25 mm translation with 12 arc sretroreflected beam deviation, the beam would have a lateralwalk off of 1.5 μm. This beam deviation has a minimaleffect on use of the interferometer for Fourier transformspectroscopy. By fitting the peak of the Fourier transform(resolution ∼0.0005 waves), a scan using steps of one redHeNe wave and a displacement range of 2047 waves mea-sured the number of yellow waves per red wave in airas 1.06543� 0.00003. Using a red HeNe wavenumber33

[in dry air at local atmospheric pressure (∼620 Torr)] of15;801.6 cm−1 leads directly to a yellow HeNe wavenumberof 16;835.5� 0.5 cm−1 in dry air at local atmospheric pres-sure (yielding 16;831.7 cm−1 in vacuum); this compares wellto the yellow HeNe wavenumber of 16;832.3 cm−1 in vac-uum assigned to the energy difference between the Ne2s22p5ð2Po1∕2Þ5s 2½1∕2�o J¼1 and 2s22p5ð2Po3∕2Þ3p 2½5∕2�J ¼ 2 levels.34,35

4 ConclusionTwo 3.3 g HRMs with clear apertures of 8.5 mm × 13.2 mm,return beam deviations of 12 arc s, and wavefront distortionsof ∼λ∕15 rms at 632 nm were fabricated and tested inactively stabilizing an interferometer. The fabrication tech-nique of directly bonding coated mirrors to each otherwhile measuring and adjusting the dihedral angle mightbe useful in fabricating other lightweight mirror assemblies.Since the reflective coating of one surface is bonded to theother mirror substrate, the coating can limit the strength ofthe bond between mirrors. Torr Seal® is useful as a structuraladhesive and should allow roof mirrors to be used within atemperature range of −45 to 120°C, but not for the cryogenicapplications of Refs. 11 and 14. Compared to the lightestcommercially available hollow roof mirrorsTM (PLXmodel RM-10-05, 25 mm × 63 mm clear aperture, 150 gmass, 1 arc s return beam deviation), these HRMs provide7% of the surface area with 2% of the mass (close to theratio expected for scaling a cube of uniform density,which does not account for the actual changes in shape, com-position, or strength). Typically, rms wavefront distortionincreases with retroreflector clear aperture, while the returnbeam deviation decreases with retroreflector clear aperture;comparisons to trihedral retroreflectors11,14,17 and hollowpenta-prisms15 are consistent with proportional scaling forboth (although fabrication difficulties increase with thenumber of mirrors). A tongue and groove joint design forthe bonded mirror surfaces11 or alternative cements11,14,24,25

might lead to improvements. It may also be possible tohollow out the aluminum base to reduce its mass15 withoutreducing torsional stability. A merit of the fabrication processis that it does not require a master optical corner cube forreference, but can be constructed using standard opticsmounts and a Fizeau interferometer.

The small size of these HRMs allows a smaller andintrinsically more stable interferometer. Assuming themotions required for stabilization are the same, the factorof 50 reduction in mass compared to commercial HRMsreduces the power required to stabilize the interferometerby a factor of 50. Further, a stabilized interferometer’sactive-feedback bandwidth is often limited by the actuator’smechanical resonant frequencies.9 Since the resonance fre-quency is inversely proportional to the square root of themass, the factor of 50 mass reduction suggests a factorof seven increase in active-feedback bandwidth. Together,these gains have enabled active stabilization of a Mach-Zehnder interferometer so that the displacement was main-tained to within �0.8 nm.

AcknowledgmentsThis material is based upon hollow rooftop mirror fabricationsupported by the Center for Advanced Solar Photophysics,an Energy Frontier Research Center funded by the U.S.Department of Energy, Office of Science, Office of BasicEnergy Sciences and interferometric characterization sup-ported by the Colorado Energy Research Collaboratorythrough the Center for Revolutionary Solar Photoconversion.

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Robert J. Hill is a defect metrology engineerat Intel Corporation. After completing a BS inphysics from Purdue University in 2000, heserved in the U.S. Air Force, working in asemiconductor laser R&D branch at KirtlandAFB. He recently completed his PhD in phys-ics at the University of Colorado, Boulder,where he worked on enabling optical technol-ogy for two-dimensional femtosecond spec-troscopy of lead chalcogenide quantum dots.

Trevor L. Courtney earned his BS in chem-istry and mathematics from the University ofFlorida in 2005 and his PhD in chemistry fromthe University of Colorado in 2012. He is cur-rently a postdoctoral research associate inthe Department of Chemistry at the Univer-sity of Washington, Seattle.

Samuel D. Park earned his BS in chemistryfrom University of California Berkeley in2010. He is currently a PhD candidate inchemistry at the University of Colorado,Boulder.

David M. Jonas earned his BS in chemistryand AB in mathematics from University ofCalifornia Berkeley in 1986, and his PhD inphysical chemistry from MIT in 1992. Follow-ing postdoctoral work at the University ofChicago, he became a professor in theDepartment of Chemistry and Biochemistryat the University of Colorado. He is a fellowof the American Physical Society, has servedas chair of the International Conferenceon Ultrafast Phenomena (Optical Society of

America), and is a winner of the Ahmed Zewail Award in UltrafastScience and Technology (American Chemical Society). His researchinterests include two-dimensional femtosecond spectroscopy and fastelectronic dynamics in molecules, photosynthesis, and photovoltaicmaterials.

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