Table Of Content1715
Optical Alignment
MitchellC.Ruda
Ruda&Associates,Inc.,8987-309E.TanqueVerdeRd.,Tucson,AZ,USA
Phone:+15205461495;Fax:+15205461481;e-mail:[email protected]
Abstract
Thephilosophicalapproachtothealignmentofopticalsystemsisdiscussed.Methods
ofdiagnosingthealignmenterrorsthroughtheobservationoftheactualimageerrorsin
theopticalsystemaresummarized.Someofthetoolsusedinthealignmentofoptical
systemsaredescribed.Importanttechniquesarereviewed.
Keywords
autocollimation;opticalsystems;opticalalignment;misalignmenterrors;aberrations;
startest.
1 IntroductionandGeneralComments 1716
1.1 WhenisOpticalAlignmentRequired? 1716
1.2 SomeImportantRecommendations 1717
2 TheOpticalAberrationsofMisalignedOpticalSystems 1718
2.1 FocusError 1718
2.2 SphericalAberration 1719
2.2.1 SphericalAberrationasaDiagnosticToolforMisalignedSystems 1720
2.3 Coma 1721
2.3.1 ComaasaDiagnosticToolforMisalignedSystems 1721
2.3.2 ATechniqueforEliminatingtheMisalignmentthatProducesComa 1722
2.4 Astigmatism 1722
2.4.1 AstigmatismasaDiagnosticToolforMisalignedSystems 1723
3 SomeToolsandTechniquesusedtoAlignOpticalSystems 1723
3.1 Autoreflections 1723
1716 OpticalAlignment
3.2 Retroreflections 1724
3.3 TheAlignmentTelescope 1724
3.4 UseoftheAuto-andRetro-reflectionstoAlignaLens 1725
3.4.1 TheOpticalAxisofaLens 1725
3.5 StarTest 1725
3.6 ThePointSource 1725
3.6.1 TheShackCube 1725
3.7 VisualAlignmentTechniques 1727
Glossary 1727
FurtherReading 1728
1 between alignment and other issues, and
IntroductionandGeneralComments (4)a realization that the alignment pro-
cedure itself is flawed and will prevent
Itisunfortunate,butthehistoryofoptics theopticsfrombeingsuccessfullyaligned.
is replete with optical alignment horror Thelistgoesonandon,butsufficeittosay
stories.Opticalalignmentisaverypracti- that everyone involved, from the project
cal‘‘hands-on’’discipline.Thegoalofthis managertothetechnicianperformingthe
chapteristoprovidethereaderwithsome alignment, would greatly benefit from an
ofthetoolsneededtosuccessfullyalignop- expandedskillsetinthisfield.
ticalsystems.Tothisend,anunderstand- To better recognize this skill set, it
ingoftheissuesthatcontributetofailure should be noted that optical alignment
andthephilosophicalapproachneededfor techniques draw upon skills learned in
successshouldalsobediscussed. many other disciplines, including optical
Often, by the time an optical system design, fabrication, testing, interferome-
is ready for alignment, the project has try, tolerancing, aberration theory, me-
exceeded its budget and is behind sched- chanicaldesign,andothers.Owingtothe
ule. With this as a backdrop, the people largenumberoftopicsthatitdrawsupon,
assignedtoalignthesystemfeelanenor- practical experience in many of these ar-
mouspressuretocompletethetaskrapidly eas is usually a prerequisite for achieving
andsuccessfully.Sometimes,despitetheir competencyinthefield.
bestefforts,theyarestymiedbecauseitis This chapter will touch briefly on
attheopticalalignmentstage,thatsomany some of the important elements of op-
alignmentandnonalignmentrelatedprob- tical alignment, general approaches, and
lems are first discovered. These typically examples of basic equipment and tech-
include the following: (1)errors in the niques.
manufactured optics and/or mechanical
parts, (2)stresses induced into the optics 1.1
because of poor opto-mechanical mount- WhenisOpticalAlignmentRequired?
ing techniques, (3)a lack of suitable di-
agnosticstoactuallydeterminethesource For the case of rotationally symmet-
of the problem(s) and thus differentiate ric systems, optical alignment ostensibly
OpticalAlignment 1717
means minimizing the tilts, decenters, 1.2
and despacings to values such that ac- SomeImportantRecommendations
ceptable image quality is obtained across
the field-of-view (FOV) of the optical Includetheopticalalignmenttasksaspartof
system. thelistofprojectmilestones:Fromthesystem
Occasionally,itispossibletotreatoptical requirements, a set of overall specifica-
componentslikemechanicalcomponents, tionsaredetermined.Thesespecifications
that is, the optics are assigned standard mightincludephysicalconstraints,optical
mechanical tolerances just like the me- performance requirements and environ-
chanical parts with which they mate. mental operating conditions. During the
A typical example would be an off-the- mechanical and optical design stage, an
shelf consumer camera lens. In such a alignmentplanshouldbedeveloped.This
case, there is usually no optical align- will help to determine the type of equip-
mentprocedureperse;thelenses,spacers, ment, tooling, jigs, and fixtures needed.
and so on are simply designed to fit Duringthetolerancestage,theaccuracyof
correctly into the lens barrel the first thealignmenthardwareisdetermined.Fi-
time. This chapter will not discuss such nally, as fabrication ofthe system begins,
systems. theactualalignmentproceduretobeused
There are, however, many optical sys- bythelaboratorytechniciantosuccessfully
tems that do not lend themselves to the aligntheequipmentmaybewritten.
aboveapproach.Anexamplewouldbean
Learn the difference between an alignment
experiment spread out over a large opti-
planandanalignmentprocedure:Theplan,
cal laboratory table. In such a case, each
whichmustbedevelopedintheearlystages
component must be brought into align-
of the project, outlines the general align-
ment separately, usually with respect to
ment approach. As an example, assume
someestablishedopticalaxis.Thesealign-
thegoalistoalignaCassegraintelescope
ment scenarios pose unique alignment
and the first step is to determine the op-
challenges. Sometimes, it is sufficient
ticalaxisoftheprimarymirror.Sincetwo
to monitor the basic set of alignment
points determine a line, the plan might
targetssuchastilts,decenters,anddespac-
require that the mirror’s center of curva-
ings, and adjust them using equipment
tureandvertexbelocated.However,since
such as an alignment telescope to fall
aCassegraintelescopeprimarymirrorhas
within specified targets. Often, however,
a central hole cored in it, it is imperative
it is not sufficient to rely on these mea-
that a method is determined and imple-
surements and verification can only be
mented before this hole is cut! Thus, the
accomplished by measuring image per-
planforceseveryoneinvolvedintheproject
formance. The question arises ‘‘How can
todeterminetheimportantaspectsofthe
an examination of the image be used as
alignment phase while there is still the
diagnostic information to determine the
opportunity to guide the manufacturing
source of the error(s)?’’ This chapter will
process.Theprocedureisadocumentthat
discuss a few of the pieces of alignment
outlinesthestep-by-stepdetailsofhowthe
equipment that allow adjustment of the
alignmentistobeperformed.
optics and will also discuss how to ob-
serveandacquiresomeofthisdiagnostic Incorporate enough adjustments to con-
information. verge to a solution: There should always
1718 OpticalAlignment
be enough adjustments to achieve the
alignment requirements, but adding too
manyunnecessaryadjustmentscanmake
thealignmenttaskconfusing.
Comfort: One factor that is rarely dis-
cussed is comfort. It is important to
be physically comfortable when mak-
ing adjustments. Consequently, the er-
gonomics–placementofadjustmentsand
viewingpositionoftheeye–shouldalways
betakenintoaccountwhendesigningthe
alignmentstation.Theuseofadigitalcam-
era and monitor to comfortably observe
imagesisalsorecommended.
Fig.1 Theairydisk
2
TheOpticalAberrationsofMisaligned about the wavefront. Unfortunately, most
OpticalSystems types of interferometers are vibration
sensitiveandthuswillnotyieldwavefront
The theory of optical aberrations in prop- data while alignment adjustments are
erlyalignedandfabricatedopticalsystems being made. Under these conditions, it
is well known. In this section, the effects is frequently advantageous to observe the
ofmisalignedopticalcomponentsonthese image of the point source–the so-called
aberrationsisbrieflydescribed.Byobserv- startest.Therefore,forthepurposesofthis
ingandmeasuringtheseaberrations,itis chapter,wewillconsiderthestarimageas
often possible to qualitatively and quanti- theprimarydiagnostictool.
tativelydiagnosethemisalignmenterrors The image of a point source, when
in the optical system. An excellent re- produced by a misaligned optical sys-
viewofthese aberrationscanbe foundin tem, can still be described by the basic
the article onOPTICAL ABERRATIONS. The aberration polynomials; the only (but im-
nomenclaturewillbethesamehere. portant)differencebeingthatcertainaber-
When a point source, located in object rations,especiallycomaandastigmatism,
space, is imaged by an optical system, it vary differently across the field-of-view
ispossibletoexaminethewavefrontusing (FOV) than they do for symmetric un-
an interferometer. It is also possible to perturbedsystems.
examine the image of the point source. The basic aberrations are now briefly
The image of the point source produced describedandtheirrelevancetomisalign-
byaperfectopticalsystemiscalledtheAiry mentsisdiscussed.
disk,showninFig.1.
The core of the Airy disk contains 84% 2.1
of the energy while 91% of the energy is FocusError
containedinthecoreplusthefirstring.
Interferometry is an excellent method Focus error (or defocus) is a very com-
for obtaining quantitative information mon type of misalignment. It is a 2nd
OpticalAlignment 1719
order wavefront aberration, given by (for 2.2
nomenclatureseearticleonOPTICALABER- SphericalAberration
RATIONS)
Sphericalaberration,a4thorderwavefront
W =W H0P2cos0θ =W P2 (1) aberration,canbeexpressedas
020 020
ThelackofdependenceonH,thefield- W =W040H0P4cos0θ =W040P4 (5)
of-view(FOV),impliesthatdefocusaffects
As in the case of focus error, the lack
the entire field uniformly. Consequently,
of dependence on the FOV, H, implies
an image that is uniformly degraded
thatsphericalaberrationaffectstheentire
acrosstheFOVmightbeimprovedsimply
field uniformly. Consequently, an optical
byrefocusing.
system that appears to produce an image
A very useful equation in optical align-
thatisuniformlydegradedacrosstheFOV
mentrelatesthewavefronterror,W,tothe
could also be suffering from spherical
resultingaxialfocalshift,(cid:2)f,bythefollow-
aberration.
ingequation:
Discerning between focus error and
(cid:2)f =±8λW (F#)2 (2) spherical aberration as the cause of
020
the image blur is straightforward. If
whereλisthewavelengthandF#isthe‘‘f- refocusing does not correct or improve
the image quality; then the error is quite
number’’oftheopticalsystem.Thefocus
shift, (cid:2)f, is also known as the depth of possibly spherical aberration. Another
way to discriminate between these two
focus(DOF).
aberrations is with the use of the star
For high-quality diffraction-limited sys-
tems, it is usually assumed that W ≈ test described in Sect.3. Figure2 shows
020
λ/4. Consequently, the maximum allow- a ray trace through the focus region of a
sphericallyaberratedimage.Thisistheso-
ableaxialshiftoftheimageplanefromits
calledcausticregion.Samplethrough-focus
idealpositionforwhichdiffraction-limited
imagesareshowninFig.3.
imagequalitycanbemaintainedis
As seen in Fig.2, when spherical
(cid:2)f =±2λ(F#)2 (3) aberrationispresent,raysdonotconverge
to a commonfocus,but ratherthey focus
If we further assume that the optical atdifferentplacesalongtheopticalaxisas
system is used in the visible wavelength afunctionoftheheightoftheseraysonthe
range,then pupil.Inthecaseshown,raysneartheedge
λ≈0.5µm
andtheexpressionreducesto
(cid:2)f =±(F#)2(inµm) (4)
As a practical example, a diffraction-
limitedf/10opticalsystem,usedatvisible
wavelengths, has an allowable depth of Fig.2 Araytraceshowingthethrough-focus
focusof±(10)2,orabout±100µm. appearanceofsphericalaberration
1720 OpticalAlignment
Fig.3 Asampleofthethrough-focusimagesofspherical
aberration
ofthemirrorfocusfurtherawaythanrays between any of the optical components it
nearthecenterofthemirror.Somewhere will most likely contain spherical aber-
between the inner ‘‘marginal focus’’ and ration. Often, it is only at the final
theouter‘‘paraxialfocus’’isaregioncalled image plane where the value is minimal
the circle of least confusion where the ray orzero.
bundlediameterisminimum. The amount and sign of spheri-
cal aberration generated by a lens is
2.2.1 SphericalAberrationasaDiagnostic dependent on a number of factors in-
ToolforMisalignedSystems cluding,shape(plano-convex,equi-convex,
Since spherical aberration is rotationally etc.),power,glassindex,etc.The amount
symmetric, it can only be introduced of spherical aberration generated by two
by symmetric misalignments. Generally or more lenses is also dependent on the
speaking, a lens or mirror will naturally lens spacings. The factors under which
generate spherical aberration for all but sphericalaberration is generatedcan also
a few special cases of conjugates and be used to diagnose both alignment and
shapes. Thus, for most optical systems, othersourcesoferrorinanopticalsystem.
when the on-axis wavefront is examined ThesearesummarizedinTable1.
Tab.1 Potentialerrorsourcesforresidualsphericalaberration
Observation Error Comment
Nontrivial(andsometimes Lensaccidentallyinstalled Acommonmistake.Often
large)amountof backwardsinthelenscell introduceslargeamountsof
residualspherical sphericalaberration.
aberrationisobserved. Reassemblelensesmore
carefully.
Incorrectairgapbetween Atoleranceanalysiswill
lensesorlensgroups determinethemostsensitive&
likelyairgaps.Checkthickness
oflensspacers.
Lensesaremanufactured Oneormoreradii,thicknessor
incorrectly indexofrefractionisincorrect
(lensmustbethoroughly
inspected)
OpticalAlignment 1721
It is not always possible to estab- common for coma to be introduced by
lish, unambiguously, the source of the nonrotationallysymmetricmisalignments
unwanted spherical aberration. However, such as tilts and decenters. In this case,
large amounts frequently indicate that a comawillbeobservedonaxis(H=0)and
lensisinstalledbackwards.Potentialspac- can therefore serve as a diagnostic tool
ing errors between lenses is relatively inthealignmentprocess.Theorientation
easyto check.Themoredifficult itemsto of the on-axis coma image indicates the
verifyareproblemswiththelensesthem- orientationofthemisalignment.
selves,especiallyifanincorrectglasstype
waschosen. 2.3.1 ComaasaDiagnosticToolfor
MisalignedSystems
2.3
Coma is the dominant misalignment
Coma
aberration when tilts and decenters are
present, for the following reason: when-
Coma, a 4th order wavefront aberration
ever two similar wavefronts are sheared
(seeFig.4),canbeexpressedas
with respect to each other, the resultant
W =W131HP3cosθ (6) wavefront is the derivative of the original
wavefront. Shearing spherical aberration,
Inanefforttoproducegoodimagequal-
which varies as P4, will produce coma,
ityoverasuitableFOV,theopticaldesigner
whichvariesasP3.Thisshearingisactually
attempts to reduce or eliminate coma.
Whilethisgoalisoftenrealized,someop- produced when the internal, spherically
ticaldesigns, such asthe Cassegraintele- aberrated wavefront impinges on a lens
scope,containinherentamountsofcoma. that is tilted and/or decentered. The lens
Nevertheless, in a perfectly aligned, rota- itself can be thought of as a generator of
tionally symmetric optical system, coma sphericalaberration,whichwhenproperly
will always be zero on axis (i.e., H=0) alignedwouldaddtoorsubtractfromthe
and if inherent coma is present, it will sphericalaberrationoftheincomingwave-
increase linearly out to the edge of the front.However,whenitisshifted,ashear
FOV. For reasons discussed below, it is occurs,producingthecoma.Sincespheri-
calaberrationissopervasiveinsideoptical
systems,thetiltsanddecentersoftheop-
ticalcomponentstendtoproducecopious
amountsofcoma.
Figure5(a) depicts the images of nine
pointsourcesacrosstheFOVofanaligned
optical system (such as a Cassegrain
telescope) that contains inherent coma.
Note that (1)there is no coma on axis;
(2)the comatic images are all radially
symmetric about the center of the FOV,
and (3)the image size increases linearly
withtheFOV.Figure5(b)depictsatypical
coma contribution (not necessarily what
Fig.4 Theimageofapointsourcecontaining is observed) to the FOV due to some
coma misalignment in the optical system. We
1722 OpticalAlignment
+ =
(a) (b) (c)
Fig.5 ImagesofninepointsourcesintheFOV.(a)FOVwith3rdordercoma;(b)misalignment
contribution;(c)resultingFOV
observeseveraldetails:(1)comaispresent theamountofcomaproducedareroughly
onaxis, clearlydue to the departure from linear with respect to the amounts of tilt
symmetry caused by the misalignment, anddecenteredintroducedbyoneormore
(2)the magnitude and orientation of the of the optical components in the system.
coma contribution is roughly constant Ausefultechniqueforremovingthecoma
across the FOV, and (3)these comatic is to provide two controls to the optical
images are bilaterally symmetric about a system.Thesecouldbethetiltoftwoprop-
vertical plane indicating the cause of the erlychosencomponents.Asonecontrolis
problem must be a tilt or decenter of a adjusted(saytheverticaltiltofadjustment
componentintheverticalplane. #1), the image will move. But the second
Whenthecomaduetothemisalignment control (say the vertical tilt of adjustment
contributions add to naturally occurring #2)isadjustedsimultaneouslytocorrectthe
coma from the optical design, images imagemotion.Onethenobservesthatthe
across the FOV depicted by Fig.5(c) can amountofcomaintheimagewillchange
often result. Here we observe (1)coma is until the vertical component of come is
present on axis and (2)coma is zero at removed. The two horizontal controls are
some point in the FOV where H (cid:2)=0. then adjusted to remove the horizontal
Usingtheseimages,thenextstepistoim- coma component. This will allow the on-
provethealignmentoftheopticalsystem. axis coma to be corrected, but does not
guaranteethattheimagesthroughoutthe
2.3.2 ATechniqueforEliminatingthe FOV will be properly aligned. Given the
MisalignmentthatProducesComa vast array of optical systems designed
Clearly, in order to eliminate the coma, today, some thought must be used in
it must be assumed that suitable adjust- choosing which two optical components
mentsareincludedintheopto-mechanical willbeprovidedwiththeseadjustments.
design to achieve this goal. Generally
2.4
speaking, when an optical component
Astigmatism
is misaligned (i.e., tilted or decentered)
two effects are observed: (1)the image
Astigmatism,another4thorderwavefront
movesand(2)comaisintroduced.Under
aberration,canbeexpressedas
manycircumstances,theamountofimage
motion(alsoknownasboresighterror)and W =W H2P2cos2θ (7)
222
OpticalAlignment 1723
As in the case of coma, the optical
designeralsoattemptstoreduceorelimi-
nateastigmatism.Whilethisgoalisoften
realized,someopticaldesigns,suchasthe
Ritchey-Chre´tientelescope,containinher-
entamountsofastigmatism.Nevertheless,
in a perfectly aligned, rotationally sym-
metric optical system, astigmatism will
always be zero on axis (i.e., H=0) and
Fig.6 Anastigmaticlineimage
if inherent astigmatism is present, it
will increase as H2 out to the edge of
3
theFOV.
SomeToolsandTechniquesusedtoAlign
2.4.1 AstigmatismasaDiagnosticToolfor OpticalSystems
MisalignedSystems
3.1
Astigmatismisalsoassociatedwithnonro-
Autoreflections
tationally symmetric misalignments (tilts
and decenters) but the presence of pure,
Auto- and retro-reflections are used,
on-axis astigmatism can also indicate
especiallyinalignmenttelescopes,toalign
other errors such as optics under stress
opticalsurfaces.Theprefix‘‘auto’’ means
from the mechanical mounts. Astigma- ‘‘self’’.Thus,theterm,‘‘autocollimation’’
tism can also be unintentionally polished refers to a collimated beam within which
intotheopticalcomponents.Onemethod each individual ray reflects back upon it-
for differentiating between these errors self. This is depicted in Fig.7(a). Here, a
and misalignments is to rotate suspected pointsourceiscollimatedbyalenshaving
lensesand/orlenscells.Iftheorientation afocallength,f,andreflectsoffofaplane
of the astigmatic line image (Fig.6) ro- foldmirror.Ifthefoldmirrorisnormalto
tates with the optics, then the optics has the optical axis of the beam, the rays will
astigmatism. return on themselves, back to the point
(a) (b)
(c)
Fig.7 Autoreflections:(a)Autocollimation;(b)autoreflectionoffaconcavesurface;
(c)autoreflectionoffaconvexsurface
1724 OpticalAlignment
source.If the mirroris instead tilted by a is detected. Retroreflections are therefore
(small) angle, α, the return image of the notasusefulasautoreflections.
point source is displaced by an amount,
ε,where 3.3
ε∼=2αf (8) TheAlignmentTelescope
As shown in the figure, autocollima-
The alignment telescope uses the prin-
tion is merely one of several forms of
ciple of autoreflections to align optical
autoreflections that can be produced off
components onto its reference axis. It
the concave (Fig.7b) and convex (Fig.7c)
consists of an illuminated pattern, usu-
surfacesaswell.
ally concentric circles that are projected
through a beamsplitter, and an optical
3.2
Retroreflections system capable of focusing from close
to the front on the instrument out to
The condition for a retroreflection occurs infinity (Fig.9). The return (see Fig.7)
when the image of the point source is imaged into an eyepiece that contains
depictedinFig.8isfocusedonthesurface a crosshair. Adjustments are made un-
of an optical component. As the surface til the bull’s eye pattern is centered on
is tilted, no motion of the return image thecrosshair.
Return from
tipped surface
Any surface:
plano
CVX
CCV
Tipped
surface
Fig.8 Retroreflections
Bull's eye return
Eyepiece FOV
Beamsplitter
Fig.9 Thealignmenttelescope
