Rochester Institute of TechnologyRIT Scholar Works

Articles

2006

Introduction to shadowgraph and schlierenimagingAndrew Davidhazy

Follow this and additional works at: http://scholarworks.rit.edu/article

This Technical Report is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Articles by an authorizedadministrator of RIT Scholar Works. For more information, please contact ritscholarworks@rit.edu.

Recommended CitationDavidhazy, Andrew, "Introduction to shadowgraph and schlieren imaging" (2006). Accessed fromhttp://scholarworks.rit.edu/article/478

INTRODUCTION TO SHADOHGRAPH AND SCHLIEREN IMAGING

Andrew DavidhazyRochester In.titute of Technology

Imaging and Photoqraphic Technology

- SI-tAbOIJ612APHS-SCHLIE'REN

-UffiRffRD6I2AHS

FOUCAULT

-TOE'PL£R.

-MACH-SCHA'RbIN

Schlieren photography is not new.It's a technique peripherallydeveloped by early astronomers andglass maker•. It is a word that hasit's origin in the german word"schliereN or streaks, caused byinhomogeneous areas in glass. Avariety of methods were used todetect these .chliere, with some ofthem probably closely related to thetechnique. which we are about toexamine.

There are three basic types ofoptical probing systems each withintrinsic merits and limitations.These are shadowqraphs, schlierenimages, and interferograms. The5e arelis~ed in order of increasingcomplexi~y and pos5ible varia~ions.

In ~he mid 1800's, Leon Foucaultdeveloped a test ~ha~ bears his namefor examining the figure or curvatureof as~ronomical mirrors. Worker5testing mirror.~i~n the Foucault~est were well aware of, and tookgreat pains to minimize, thedisturbing effects of densitygradients present between the lightsource, the mirror and the "knifeedge".

Some of the pioneers in terms ofdevelopment of applications were suchpeople as Toepler, Mach, Schardin,and others.

REFRACTION

Speaking in broad generalities, mostapplications of shadowgraphs andschlieren techniques have mainly beendeveloped in the field of ballisticsand aerodynamics, although manyapplications have been developed tostudy fluid mechanics and thermalexchange processes.

The fundamental principle behindshadowgraphs and schlieren opticalprobing systems i. that light raystravel in space or transparent mediain straight lines unless theirdirection is altered by someobstacle. Interferometric systemsusually depend on a phase shiftassociated with changes in thevelocity of light.

::~ ~.:.. :. ~..- -r " ..•, :... ,~.1"" :,-•.. • .. i

By way of brief summary. the changesin direction which light rays canundergo are summarized as follows:

Upon entering at right angles to thefirst surface of a medium of uniformdensity and paralell sides, the ligh~

ray slows down or speeds up as itgoes across the medium, depending oni~'s density, but it's direction isnot altered. Upon exiting it picks upit's original velocity.

If the ray passes through a similarsubject at an angle, then it'sdirection is altered upon enteringthe first interface, but if it exitsinto the same medium as the one itentered from, then it returns to it'soriginal direction at the exitinterface.

If the intervening area does not hav~

paralell faces, then the liQht raywhich enters the region of differentdensity has it's direction changed asabove but since the exit interface isnot paralell to the first one, theexiting ray does no~ pick up it'soriginal direction but assumes a newone.

IIIII

5"

Also. when light rays travel in thevicinity of a region where there is achange in densi~y AS shown in ~he

illustration, the direction of thoserays p~ssing clo.e to this ~rea willal.o suffer a ch~nge in direction.One could oversimplify this effect interms of simply thinking that thoserays which move past this region"stick" to the denser medium belowand thus affect the direction of theray or rays passing in this vicinity.If the denser medium is located ontop. then the rays bend upwards.

For all tes~ method•• a liQht sourceis required. Light will emana~e fromthis source in all directions. Fornow we will deal only with a "poin~"

source. although a true point sourceis often not obtainable or desirable.

When light from this source falls ona screen, the screen will appear tobe lit up by the light rays fallingon it. If the source is very far awaythen the change in distance between~he source and the edges of thescreen will be negligible. This willresult in an energy distributionwhich is shown in the drawing. Thatis, there will be the same units ofenergy per unit surface area. Thiswill be reflected by the visualsensation that the screen appears tohave the same "brightness" orluminance allover. We could .implysay that on any given spot there isone light ray falling. In ~his case,over the five points shown, we wouldmeasure one ray over each point. orfive total units of light energy.

---Jo2II

5

If we now disturb ~he 5itua~ion andalter the path, or flight direction,of ooe of these rays, w. will noticethat the energy distribution patternhas changed. From one place the lightray is removed, with the illuminationfalling to zero, and at another, thelight that was taken from theprevious point is added to that pointwith the consequence that theillumination is doubled. This areaappears twice as bright as theundisturbed ~urround.

Notice that the total energy hasremained unchanged. We have simplytaken some energy from one place andmoved it to another. We have.however, set up a system fordetecting th. fact th~t somedisturbance located between the light~ource aod the screen has appeared,changing a ·steady state- condition.The exact location and magnitude ofthe disturbance is hard to pinpoint,however.

'R.£SOLUTIOt-J

• ])ECIUA5E UQIT ~R';: SIZE"• SHALl. SOUllC£' - SCR[OllllSrAAC[

5~NS'TIVITY

• L~l: SOUllC[-SCIlEEN llI$TANCt

The sharpness of the images securedwith this type of detection systemdepends largely on the size of thesource, the smaller the better. Also,as the distance from the source tothe screen increase~, the sharpnessof the shadow image formed increases.Sensitivity, on the other hand,increases a5 the distance between thedisturbance and the screen increases.Sensitivity and resolution depend onopposing parameters.

Generally, in what could be calleddirect shadowqraph recording, thescreen is a piece of photosensitizedmaterial the size of which limits thesize of the subject that can beadequately recorded on it. If this isthe system design, then the work mustbe carried out in a darkenedlaboratory .

r • <0 •. .... "

..

. . ., .

.' . . ..'. .. ., .' ...' . . . .. ..... :: ... :":~.'•• :'::"" .0

4

......... -.....::: .. :.: ..... ;.",'. .,.' . '.,. :.~' .-....:.... :::.

:: :: ':.-.:',':', :.:., •• :::' ":. I""· ., .'. ,,', :. '. ", '. .' "" .. '., '. '. '. ..' .'.. ', ... .,. .' ,::. : " " ,,',.,. '" .'. " ..

'. . . i:' . .•.• •'.' " \ . ', ,' ::·.' , , ....' . \'. ' ..' ' ., ... ...... I····:.·.·~·

• " 0' ... ,.' '. :'" .. . . '.. ' ~."..::::.: .•• , ...... : •• : •••• " .'~ •• 0'.'. . . .. '. . ..... ..." .... ' .. , . ".': ." . " .. , ..' ..

',' '. : : ;.:..: :: : ::: .. :":'.':", ". ': :.:.:: ".::::.~' .. .. '. . '.'

Where ~hR screen size is insufficientto cover the subjec~, an indirectmethod can usually be employed. Thisconsists of photographing the5hadowgraph pattern with & more orle.s "standard" camera. This isaccomplishRd by causing the patternto fallon a whi~e screen and,usually, photographing from behindthe disturbance. This, however,causes the subject it.elf tointerfere with the view of thescreen. Keeping ~he camera/light axisas close a5 possible minimizes thiseffect. An al~.rnative is tophotograph the shadow pattern frombehind a translucent ~creen .

Gains in luminous efficiency andevenness of illumination on thescreen can be accomplished bycollimating the light source. This,however, has the effect of limitingthe field size, and thus the subjectsize which can be recorded by thesystem.

A big advantage of the shadowgraphsystem is that it is relatively cheapto set up and that it can deal withsubjects of relatively large size.Attempts to increase the systemsensitivity invariably raise the costand the improved versions usually.tart to become very similar toSohlieren systems.

A further modifioation of theshadowgraph, and one which starts toapproach the principles of Schlierensystems, employs a retroreflectivematerial as the screen to increasethe luminous efficiency.

5

The "Sco~chlite" material used as thescreen has the property of reflectinglight incident on it back in the samedirection it arrived. Thus, a smallcamera located next to the lightsource will collect a relativelylarge amount of the light emitted bythe source if it is located veryclose to the source itself.Disturbances between the source andthe screen will alter the directionof the reflected light rays causingthem to bypass ~he camera lens. Theareas from which the light is thusremoved will appear dark on the imageof the Scotchlite screen. Some areas,on the other hand. may marginallygain brightnes•. Thi6 method has beenused in full daylight conditions tosecure technically useful datarelated to explosives and ballisticsbehavior.

While Shadowgraphs and Schlierentechniques are both used to studyrefractive index changes in a varietyof subjects, Schlieren systems areparticularly useful when highsensitivity is required or when acolor record is desired. Schlierensystems actually are nothing morethan Shadowgraphs in which thedeflected rays are interefered within 50me manner, rather than allowingthese rays to reach the imagingscreen undisturbed.

To understand ~he principle on whichSchlieren sys~em~ work consider thata lens makes an image of every pointin the subject by collactinq a coneof light emanating from each subjectpoint. The size or area of the baseof this cone is determined by ~he

size of the lens aperture. For agiven image size, the larger the basedimension, the brighter the image onthe '!Screen.

:

Thus, ~s a lens i. stopped down we doDot see the edges of the diaphragmdecreasing the field of view orcasting • noticeable shadow on thegroundgl.ss of a camera'. viewfinder,but rather we simply 5 •• that theluminance or brightness of the imagedecreases simultaneously overall asthe aperture is decreased.

It is interesting to note that theaperture can, in fact, b. locatedanywhere in the diaphragm plane andthe .ffect is the ••me. That is, nomatter where the aperture is, a fullimagR of the subject will be formedat the film or scr.en plane and thatit'. brightness will simply becontrolled by the open area of thediaphragm.

In fact, one could carry this processto the ultimate end and logicallyfigure out that it would betheoretically possible to make theopening ~lmost infinitely small.Then, the diameter of the aperturewould be as sm~ll as one light ray.However, even if this were the case,a ray em~natin9 from a point on thesubject would manage to pass throughthis "hole" ~nd fallon acorrespondinq location on the screen.

Actually, in this assumed state, onelight ray from every point on thesubject side of the hole would beable to pass through it and arrive atthe screen. Thus, a "standard",upside down, reversed left-to-right,image of the subject will be presentat the screen. This ultimately meansthat every point on the surface of alens produces a complete image of theSUbject.

7

The more "points" t.here ~re t.o forman image, and this is governed by thetotal Area of the lens, the brighterthe combined image formed by thecontributions of the individualcomponents or lens surface point.beeom••. Thus, the larQer theaperture the brighter the imagebecause more points on the lenscontribute their individual images tothe final composite. In graphicalform this is shown by the size of thecone of illumination at each imag_location. In photographic terms wedeal with this tact every time weadjust the f_ of the lens.

Now, assuming that we start with asource on the left, the lens makes animage of this source on the right,and the light continues onward untilit is intercepted by a screen.

- r

The brightness of ~ point on the5urf~ce of the lens is affected .5explained above and is a function ofthe size of the source and it'sbrightness or luminance. Thus we candraw rays extending from the limitsof the source to represent the coneof rays that illuminate. a qivenpoint on the lens surface.

II-3

As the.e divergent rays le.ve thelens surface, they all pass throuqhthe focal plane of the lens at theplace where the image of the lightsource is located. Eventually theserays fallon the screen and notethat, as before with the shadowgraphsystem, we can, in this verysimplified diagram, deduce (andmeasure) that the illumination levelis unity in each of the three sampleareas on the screen illuminated bythe three different points on thelens surface.

Next, the direction of ~h8 beamemanating from the middle point onthe lens is altered by some means.This causes the light beam to fallsuperimposed on the same spot as thebeam from the lower point. Theconsequence of this is that thebrightness distribution on the screenchanges. At the top we measure twounits of energy, in the middle none,and the bottom spot remainsundisturbed. The total energy stillis three units as before but itexists in a redistributed state. Fromthis new pattern which is visible onthe screen one can tell that lightwas bent away from the middle spotand added to the top spot on thescre.n. That is, a disturbance whichchanged the direction of the lightrays caused this change.

This caD then be attributed to arefraction of the light beam as ittraveled between the source and thescr••n. The location and magnitude ofthe refractive gradient which causedthis change in brightness is hard toestimate because similar totaleffects can be achieved by a smallgradient over a large distance or alarge gradient over a short distance.Plus the disturbance can be located,&5 shown here, anywhere along thelight beam for that matter. Up tothis point we have simply set up ashadowgraph system once again.

oI-2

Note that an obstruction can beplaced next to the location of theimage through which all light beamsradiating from the lens's surfacepass. Thi. will have no effect on theundeflected rays, but those that arebent will fallon this obstructionand fail to arrive at the screen.Thus, the bent light is simplyremoved from the screen and not addedsomewhere el••. This interaction ofdeviated light with an obstruction isthe principle on which the Schlierensyste. operat••. Notice that in thisconfiguration, the image formed onthe screen is a shadow image and thatit is usually quite uDsharp.

Q

We will now examine the processfurther and improve on it's sharpnessas we discuss focused systems. Here asecond lens is added behind the imageof the light source formed by thefirst leos, commonly called a "fieldlens", or flfield mirror" in mirrorsystems which will b. discussedlater. The term "schlieren head" isoften used instead of ~field lens".

v

-

The ray. of light emanating from onefield lens point are intercepted by asecond lens, the camera lens. It'sfocal length does not matter. It ischosen to simply provide an imagesize of the field lens which isadequate for the purpose. This cameralens, when focused on a point on thesurface of the field lens, willreproduce that surface point as asharp image point on it's scr.en.

As discussed earlier, the brightnessof any point on the field lenssurface, and as a result thebrightness of corresponding imagepoints, is a result of two factors.For a given brightness of the lamp,the brightness of image points can beincreased by incre.sing the size ofthe source, effectively increasingthe cone of illumination reachingeach image point in a similar manneras if the diaphragm of a camera lenshad been opened up.

Alternately, for & given source sizethe brightness of a point on thesurfac. of the field lens can bechanged by varying the sourcebrightness. This can be accomplishedby a voltage change to the filament.

10

v

Aqain, no~e tha~ the second lensreproduces each point on the fieldlens's surface. In this case it formsan image on the lower edge of thefield lens at the top of thescreen ...

... and in thi~ case it forma an imageof a field lens point located high onit's surface at the bottom of thescreen ...

.. . and now three field lens pointlocations are shown simultaneously.If the process were extended toaccount for all light rays, again wewould notice that the brightnessdistribution on the screen isuniform.

,-

Now, an opaque obstruction extendipgfrom the top dowDwards is placed at alocation close to that of the surfaceof the screen .. ,

... this obstruction blocks thoselight rays that would have fallen onthe top portions of the screen butdoes not affect the brightness of thescreen below. The ob.truc~ion

basically casts a shadow of itself onthe screen. Some of the light isactually eliminated from reaching thetop of the screen.

If you were to look at thegroundglass located at the screenposition you would see the top of theimage of the lens go dark. The shadowwould appear to come down from thetop as the mask is lowered.

\I

- -- - ---

KNIH' EDG-EMUST !IE l'LACn AT

fOCUS OF J=lfLl) LENS

Now, vakiDQ the same mask to alocation near the field lens, wewould notice that as the mask againis lowered from the top, we wouldstart to cover up the surface of thefield lens from the top. This isrefl.cted at the final image plane.within the camera, as a gradualdarkening of the image starting fromthe bottom. The unaffected points onthe field lens surface will notchange in brightness because they canstill beam the totality of the lightrays which come from the source.

The visual impression apparent at thescreen, then, is as shown here, withdarkness appearing to move upwardsnow even though the opaqueobstruction is moving downwards aswas the case above. One might ask,then, whether there is a place thatthe obstruction, commonly called a"knife edge", can be located at whichthe inflexion, or reversal ofdirection of shadow motion, occurs.With the knife edge at this locationone should not notice the directionin which the shadow is moving butwould rather simply perceive agradual darkening of the image of thefield lens on the camera'. screen.

The location at which the knife edgecauses this gradual overall darkeningwithout giving a hint of thedirection in which it is beinginserted into the light beam is whenit is located at the exact focus ofthe field lens. This point or planeis sometimes referred to ~s theschlieren plane or stop. All we havedone so far is to set up for aFoucault test of a lens l •

In these illustrations the image ofthe light source is shown falling onan improvised knife edge with thewhole image falling on theobstruction ~ In practice a small<'Vamount of light is allowed to pass bythe knife edge to give the backgrounda noticeable tone. How this isaccomplished is discu~sed next.

12

Referring to an earlier illustration,we discussed that the brightness ofany given point in the image could bealtered by changing the source size.Th~ exact same effect can be producedby changing the size of the image ofthe source. This is what happens whenthe knife edge is inserted at theexact focus of the field lens. Bytaking a single point on the surfaceof the field lens a~ an example, youcan see that the insertion of theknife edge cuts into the beam oflight coming from the surface of thefield lens. This results in a fewerlight rays reaching the correspondingimage point on the screen, thuscausing the brightness of that pointto fall. The effect, again, isexactly the same as if we haddecreas~d th~ size of the sourceitself. Basically, if the knife edgecuts 50% into the beam theillumination level at the screen willdrop to 50% of ~he original level.

Just to carry the point a bitfurther, note that since the lightrays from all points, here summarizedwith just two, pass through the imageplane of the field lens, the knifeedge will simultaneously cut into theimage of the source formed by thecumulative oontribution of all pointson the lens surface. At any otherlocation along the beam, the knifeedge interferes more with some of theimage beams than others causing anuneven darkening of ~he image of thefield lens. Therefore, with the knifeedge in this location, the brightnessof every image poin~ i. diminishedsimultaneously. The visual appearanceof ehis process of cut~ing into theimage of ~he light source, then, isas shown in this illustration.

/3

FOCUS OF FIHD LENS

VARIf:5 WITH

WAVELEN6TH

:=-:::::-._ UWDt\ftlr&U

_. _ J)~rulle..'"

A~ ~his point it may be appropriateto mention that if field lenbes areused, the schlieren field may appearcolored even with no disturbancespresent.

This is due to the fact that unlessthe field lens is free from chromaticaberration, it's focal length, thusthe location of the sharply focusedsource image varies with wavelength.Since the knife edge must be locatedat the exact focua of the lens thiscaD only be achieved perfectly forone wavelength. This means that allother ~harp images of the sourceformed by the other wavelengths willbe out of foous at the knife edge.This caU58S an uneven distributionfor .11 wavelengths other than theODe which is sharply focused at theknife edge. This then causes anunev&n distribution of colors toappear on the screen. This is one ofthe rea.ons that high quality concavefirst $urface mirrors are usedinstead of lenses since mirror opticsdo not suffer from chromaticaberration.

At this point we will look at asituation in which the light from apoint on the field lens travelsundeviated and deviated paths throughthe system. When the beam isdeflected from its normal path bysome disturbance at the point oforigin of the beam as it leaves thelens, the beam may be deflecteddownwards as shown in this example.This now forms an ima~e of the lightsource below the point where all theother images are form_d by theseother points on the surfaoe of thelens.

A. ~hiw deviated ligh~ beam continuesto travel towards the right all of itis intercepted by the second, camera,lens. This lens "sees" the liqh~

coming from the same spot on the lensas an undevia~ed beam would cometrom, and thuw proceeds to place ~he

light in this deviated beam in thesame spot that it would place theligh~ from an undeviated beam.

This i. no~ the case, however, if thedisturbance happens beyond theradiating surface of the field lens.Then, the second lens sees thedeviated beam as coming from adifferent location on the field lensthan an undeviated beam would comefrom. Thus, the light ends up in adifferent location than ~he one atwhich the undeviated beam would havearrived. This cau.e. the subtractionof light from one location and theaddition of this light to anotherlocation ... a shadowgraph.

UMDtSTP.IS.

t)l,tuaa',.

If now, in the steady state orreference mode, a knife edge isintroduced just below the image ofthe source then the screen will stillappear as bright a. it possibly canbecause all the light from everyfield lens point i. collected by thesecond lens without in~erference.

However, if as shown, the beam from agiven point is deflected downwards,in that case the deflected light isstopped by ~he knife edge and it is,in this case, totally eliminated fromthe screen. That spot on the image ofthe field lens goe. dark. If thedisturbance is not at the surface ofthe field lens the image of the spotfrom which the beam emanated darkensanyway. Notice that as was the casein a previous example, in thi. casethe refracted or deviated light iscompletely eliminated from ~he

system. Unlike a shadowQraph therefracted light is IOlowt lO

, a~ leastto tne screen. A••tated earlier,this i. the operating principle of ascnlieren system.

__ UIolIlt~TlJaet'D

_._ J)l"TUR~£»

__ lI'W~l\IU(l)

_._ l)1!.1V1lt.'D

Now let us set up the system so ~hat

half of the sharply focused image ofthe source is obstructed in thesteady state condition. Then allscreen points in the camera becomehalf as luminous as they can possiblyget. Now, when the upper beam getsdeflected away from the knife edge ata point in the field lens, the imagewhich this point would havecontributed at the knife edge is ableto pass the edge completely but eventhough it has a Dew direction all ofthe beam is intercepted by the secondlens. As above, this lens sees thelight coming from the point at whichthe beam was deflected and thus itplaces all the light in this beam ODthe corresponding image point OD thescreen. This point will now appear asbriqh~ a~ it there were no knife edgein ~he system at all. Again, unlikein shadowgraphs r note that screenbrightness at this point goes upwithout a corresponding loss ofillumination at some other point.

If, as is more usually the case, thedisturbance does not happen in thefield lens, then the second lens willplace these deflected image formingrays in a different spot than ~he onethey belong to. This means that thespot from which ~he beam emanatedwill darken. Further, however, thespot from which the second lens seesthe deflected rays coming from, willincrease or remain unchanged inbrightness. The latter happens if thesource image is comple~ely blocked bythe knife edge. Again, a shadowgraphin nature. The knife edge, however,interacts with the deflected rays asthe image of the source moves acro.sit. A schlieren characteristic. Thus,schlieren and shadowgraph arecombined on one optical system inthis manner.

Therefore, shadowqraphs and schlierensystems are quite in~errela~ed. Itcould be said that a true schlierensystem can not exist unless theregion of refrac~ive index gradientscan be confined to the field lensplane.

16

Two interesting, and popular,variations on the hard edge techniquediscussed so far follow. The first.merely replaces the opaque knife edgewith a transparent colored filterarray. A simple but popular arrayCOD§lsts of filter material arrangedas shown here and placed in the planeof the knife edge.

•»-::>;~ -,r-~ "V

aBED

Note that in 'this "color" schlierensystem all the undeviated rays aremade to pass through a narrow, blue,oentral filter band. Thus, theschlieren field as seen on the screenof the camera acquires an overallcolor of blue. When a beam isdeviated from it~ normal path andbent downwards, it moves so that moreand more of it passes through the redfilter with that spot OD the screenbecoming first magenta and eventuallycompletely red. Conversely, if ~he

beam is deflected upwards, the 5potbecomes first cyan and eventuallyturns totally green.

It should be mentioned ~hat

disturbances which cause the beam todeflect farther than the limits ofthe diameter of the second lenscompletely disappear from view andnot only do those areas go totallyblack on the screen, the light whichbelongs to those areas obviously cannot be added to any other spot on thescrelln either.

. ... . .....•. ,...... ,

Again, if the disturbance ocurrs awayfrom the field lens surface the lightenergy from a given spot will beadded to another point on the screen.If the deviated light g08S throughthe green filter but it appears tocome from a normally red region, thenthat area on the screen will appearyellowish, while the area from whichthe beam actually is coming from willdiminish in intensity.

A second variation is pO.5ible bysubstituting a soft edge, orgraduated filter for th_ hard edge orthe color array. This scheme isparticularly useful if there arelarge changes or gradients indensity. Further it tends to resultin improved sharpness due to alessening of diffraction effects aslight interacts with the sharp hardedge, or the hard color edges of thecolor filter array.

,..~~ v

One simply replaces the hard knifeedge with a graduated density filterand moves this filter with respect tothe image of the light source untilthe image of the field le05 assumessome desired brightness level .Refraction of a particular beamacross the filter will cause theimage of the source to pass throughmore or less dense areas of thefilter. This results in a decrease orincrease in illumination of thepoints which correspond to thelocations which the light in thesebeams represent. Since the light beamdoes not interact with a .harp edgediffraction effects are lessapparent.

Further, since the contrast of thegraded edge can be made steep orshallow, the sensitivity of ~he

system can be extended over a largedynamic range with. shallow contrastfilter. A sharp oontrast gradedfilter starts to behave more and morelike a regular knife edge andsensitivity and dynamic range are forall intents and purposes controlledby the size of the source. Thesmaller the size of the source in adirection perpendicular to the edge,the greater the sensitivity and thesmaller the dynamic range.

The sensitivity of a schlieren systemis also dependent on the field lensor mirror focal length, the longerthe focal length the greater thesensitivity. Actually, what mattersis the distance between thedisturbance and the knife edge. Thiscan obviously be made greater withincreasing focal length sosensitivity is tied in with focallength in this manner.

/ SAME &RA1l1Ef(!"/

/

I.

---C~-~ 2.-

TOTAL ~EfLE(TIOIJ POo;SIBlEaEFORE I'A>l6-E ElUIAUSTtD

COLOlt

In terms of sensitivity black andwhite system~ seem to me to be moresensitive, but at the expense ofdynamio range. On the other hand, thedynamio range of color systems can belarge while retaining a respectablelevel of sensitivity. The reason forthis is that in the color system theimage of ~he light source can 'travelacross ~ number of transparentobstructions continuing to yieldinformation about the interactionbetween the image of the source andthe series of colored filters. in theblack and white system the image ofthe light source can only bedispl~ced over a distance equal toit's width before exhaus~inq therange of tones it is capable offorming at the camera's screen.

One most interesting effect, and oneWhich dramatically illustra~es thepoint ~hat most schlieren systemsbasically consis~ of two superimposedoptioal systems, is apparent when theaperture of the second lens isaltered. Notice that unless thediaphragm is closed ~o a very smallopening, changes in the aperture ofthi5 lens have no effect on the lightbeams which form the image of ~he

light .ource at the knife edge. Thismeans that as far as the schlierenfield is concerned, its brigh~ness isaffected only by the size andbrightness of the light source. Thebrightness of ~he "silhouette" of thesubject is controlled by the apertureof the camera lens and the lightfalling on the .urfaoe of the subjectlocated in the schlieren beam.

By adding lighe to an opaque subject,which may be cau~iDg density changesnear i~, the surface of the subjectbecomes vi9ible without thebackground, or schlieren, field beingaffected. The three images shown herewere taken at decreasing aperturesbut a~ the same exposure time. Notethat ~he visibility of the candleflame becomes less as the lens isstopped down but that the backgrounddensity remain. unchanged.

Now we will briefly review theoptical layout of a single field lenssohlieren system. The source consistsof a compact, rectangular lightsource with well defined edges. Ifthis is not available, a larger andless regular source can be reduced insize and shaped by passing it througha slit which may have variable widthcapability.

The filament of the lamp, or theslit, is located at roughly ~wo focallengths from the field lens. Thisforms a life size image of the sourcealso two focal lengths on the otherside of the field lens. The knifeedge or filter array is located atthis plane. It is moved back andforth until the image of the sourceis sharply focused on the knife edge.A camera lens is located somewherebeyond the knife edge location makingsure that the diaphragm of the lensis wide open or at least that thediaphragm does not interfere with ~he

ligh~ rays which form the image ofthe source at the knife edge. Withautoaperture lenses it is best to setthem in the manual mode. Some workershave used the edge of the actualcamera len. diaphragm as a substitutefor a separate knife edge withsuccess.

If the camera lens is aimed at thefield lens and focused on the subjectplane which should be as close to thefield lens as possible. Then, a fullyilluminated image of the surface ofthis lens should be visible in theviewfinder.

7n

As the knife edqe is inserted intothe beam the illumination shouldgradually diminish overall. If acolor fil~er array is inserted in thebeam, then the field should acquirean even color made up of the color ofthe central filter band when thelight which forms the image of thesource passes through it. Fields ofuneven brightness or colordistribution Are qenerally consideredtechnically imperfect in theiralignment and set-up. When thesubject is placed in it's properlocation it will show up insilhouette against the background.

It is also possible to set up a "darkfield" schlieren system by making theknife edge block all the rays in thesteady .tate condition. Then, onlybeams which are bent away from thee4ge will a4d light to correspondingimage poin~s in the viewfinder. Or,the knife edge can be a strip, or acircle, if a circular source is u5ed,which just blocks the image of thesource. Then, ~ny movement of theimage of the source across ~he stripwill add light to the 9roundQlass.With the circular knife edge movementin any direction becomes detectable.

2;

Now we'll look at the l.yout for asingle mirror type schlieren system.Besides the freedom from chromaticaberration, mirrors have the addedadvantage over lenses that they needto only have one surface ground andpoli.hed and th.t defects in thesubstrate are usually of much lesssignificance. Thus large diame~er

mirrors are considerably lessexpensive and better than lenses forSchlieren applications.

21

In this system the basic layout ofdistances and alignment procedures isthe same as with a single lenssystem. However, since the light isreflected by a mirror, the bendinqangle caused by the light passingthrough the density gradient locatedin front of the mirror is doubled inmagnitude. Thus, this type ofschlieren system has twice thesensitivity of • lens type system ofequivalent focal length. It is knownas a double-pass or 2X sensitivitysystem.

The gain in sensitivity of a singlemirror or two-pass schlieren systemis not achieved without penalty.Notice that the axis of illuminationand the axis of view are notcoincident. Since there i5 a smallseparation b.tween the two, thesubject obscures part of the mirrorsurface from the light sourceessentially c ••ting a shadow on themirror surface. From the point ofview of the recording camera, thesubject covers up a different portionof the mirror surface. These effectscombine to produce what appears to bea double image of the subject at thecamera. These are actually thesubject and it. shadow. They can bemade less objectionable by keepingthe separation between the source andthe camera lens small. There areschemes whereby the two can be madecoincident, but only at the expenseof light available in the system.

Thea. examples show that the colorsvisible in a color schlieren systemare totally dependent on thearrangement of the filters used inthe system. As mentioned earlier, asf~r a. sensitivity is concernedtheoretically, there is no intrinsicadvantage in a color vs. a black andwhite record other than we ~re ableto distinguish differences in coloreasier than differences in tone. Theadvantage of color systems liesprimarily in the extended range oflight beam deviations they canaocomodate without stopping to yieldu5eful information.

If

The most popular type of schlierensystem is the "Z" type and 'this isthe type that is most often used inconjunction with wind tunnel studies.The liqht source used has the samerequirements as for systems presentedearlier, however. in this layout itis located to one side of one of thetwo schlieren mirrors and exactly onefocal length away from the mirror.Because of it's placement in thisposition, the mirror projects a moreor less paralell beam of light, as iftrying to focus the light from thesource at infinity. The location ofthe source, in fact, is adjusteduntil the emerging beam from themirror maintains the same diameterover an extended distance.

A second mirror, which can be locateda cODsiderable distance from ~he

first, thus allowing the wind ~unnel

to be placed between them, interceptsthe light beam from the first mirror.Because it is paralell and thereforeappearing to come from infinity, thesecond mirror bring5 this light to afocus, and forms and image of thesource one focal length from it'ssurface. The mirror is turned so tha~

it places the image on the oppositeside of the beam as the location ofthe source. This placement tends toreduce aberrations introduced by thefirst lens being at an angle to thesource.

While the placement of the knife edgeis standard, the distance of thec~mera to the image pl.ne will needto be adjusted so that the lens isnearer to the image plane than whenfocused on infinity. Most standardcamera lenses do not allow this andlenses on bellows need to be used.

The reason for the unusualrequirement mentioned above is thatthe second schlieren mirror acts asan auxiliary optical element withrespect to the light rays that makeup the image of the object located inthe schlieren field.

13

When the subject is located exactlyone focal length from the mirror, themirror in effect projects the imageforming raY5 to infinity. The.e raysarrive to the camera l.ns as such andthis lens will ne.d to be set toinfinit.y focus.

When the subj.ct is located fartherfrom the mirror than one focallength, then the mirror brings theimage forming rays to a real focusand the rays leave t.he mirrorconverging t.owards this focus pointwhere a real invert.ed imaOR of t.heschlieren field will be formed. Sincethese rays are converging when t.heyarrive at the camera lens, and t.hecamera lens-to-screen distance isle••t. when the incident rays from asubject. are paralell, t.he lens will,in fact, form an image of the subjectat a di.tance le•• than that which ithas when the lens i. focused atinfinity.

It i. only if the schlieren field islocat.ed at. a dist.ance smaller thanthe focal length of the second mirrorthat the camera lens will need to beracked out. beyond it'. infinity.et.ting. When t.he subject. is locatedhere, then the diverging angle of theray. from the subject i. reduced inmagnitude but they l.ave the mirrorstill diverging. Thus when tha cameralan. intercepts them the lens willneed t.o be extended beyond itsinfinity position.

Generally, the schlieren field is notlocat.ed so close t.o the second mirrorbecause it's location here wouldintroduce aberration. and possiblyinterfere with t.he light source••••mbly. In addition, one of theprimary advantage. of t.he doublemirror system i. exactly that thedi.tance between t.he mirrors can bekept large to introduce object.s aslarge a•• wind t.unnel between them.

.ll'~TER--[I~AAKER

It 1s worth men~ionin; tha~

shadowgraph and schlieren systems arenot representations of absolutetemperature or density of a medium.Thus, they can not, for example,distinguish warm air from cold air.All each can do is ~o detect an edgeor a gradient. That is, if it isestablished that there is in ~he

subject an area which is warm, thenproceeding from the left, forexample, one will run first into adensity gradient going from high tolow. This may cause the image of thelight source to move away from ~he

knife edge thus this gradient willappear brighter than the surround.

Conversely, as the other edge of thewarm area is traversed, one would 90from a low density area to a highdensity one. This will cause theimage of ~he source to move in theopposite direction as in the previouscase. Therefore, this gradien~ willappear as a darker area on thescreen.

Also, it should be no~ed once morethat ~he reverse dis~ribution of.ubject tones, or colors in a colorset-up, can be secured by the simpleexpedien~ of reversing the positionof the knife edge.

In a simplified subject asillustrated here, areas of uniformdensity regardless of whether theyare high or low or in between, willappear &s areas of uniform brightnessat the final image. It bearsrepeating that shadowgraphs andschlieren systems detect edges,ohanges, or simply gradients, whichcause a deviation in the path oflight rays whioh travel through theseqradieD~s.

25"

SHADOWGRAPHSsc.HLIERE.I\I

So far we have covered quite standardapplications of shadowgraph andschlieren systems. The applicationsall deal with imaging densitygradients in transparent subjects.These density gradients alter thepath of light rays and these deviatedrays rearrange the light energydistribution on a screen for theshadowgraph system, or interactpositively or negatively with a knifeedge in a schlieren system to producebrightness or luminance changes at animage plane.

~;

...·f

~:' .....

RfFLECTION

=6

Both systems depend on altering thepath of light rays by "refraction".But the path of light rays can alsobe altered by "reflectioo", Thus itshould be possible to also designreflection shadowqraph and schlierensyst.ems .

First we need a source and ~hen areflective subject. This willinvariably be some kind of amorQ-or-less-fla~ surface. The lightr~ys from ~he source reflect. off thissurface and proceed to fallon ascreen as in a typical shadowgraphset.-up. The brigh~ness of ~his screenwe will assume is rather uniform.

When a dis~urbance appears whichal~er9 the flat.ness of t.he subject'ssurface, light. rays assume new flightpat.hs or directions depending on theangle at which t.hey fallon theuneven surface. Since their directionis altered, they fallon new areas onthe screen and change t.he brightnessdistribution ... but not the ~otal

light energy falling on the screen.Suffice it to say that the newpattern formed on the screen is adirect indication of the fact thatthe surface is no longer flat.

,..:',,'l-~:::-----, '"..

A similar scheme can be set up wi~h aschlieren system, with the surfaceunder study made to interact with theschlieren beam in any of a number ofschemes. We will set up ~ systemwhich might be used to .tudy thesurface flatness of a solid subject.

The light source i. placed one focallength from a lens, The light beamleaves this lens essentially in aparalell collimated beam. The beamreaches the reflective surface.Assuming that the surface is trulyflat, the beam is reflected equallyat every point and heads back towardsthe schlieren head or lens. If thesource is placed exactly on axis, andthe surface is perpendicular to it,then the reflected beam will bereimaged on the source. Since this isnot generally ~ useful lOCAtion, thesource should be located slightly offaxis, causing the reflected beam toform an image of the source slightlyoff axis on the other side. This isthe location for the schlieren knifeedge, with the camera lens locatedslightly beyond the edge as in aregular schlieren system.

Introducing the knife edge into thelight source image here ha. the sameeffect as in a transmission schlierensystem. The overall field brightnesschanges as the knife edge i. made tocut off more or less of the image ofthe light source.

:: ... ,....','"'.

If the surface contains areas whichare not flat, then the slope of thesurface will cause the image of thelight source to move .with respect tothe knife edg•. If a point causes theimage of the source to move towardsthe knife edge, then that area of theimage of the surface at the camerascreen will darken. Conversely, ifthe image is deflected away from theedge, then that area will lighten. Ifthe image is deflected along theedge, then the area causing thisdisturbance will darken while anadjacent area will lighten. Thus, theschlieren and shadowgraph systems aresuperimposed on each other.

27

FLAT?

.~...:";::..

llEfLiCT IoN

In fact, not only are the two opticalsystems superimposed on each other,but it is even possible tosuperimpose the refractive andreflective configurations on eachother as well. A typical applicationfor such an arrangement would be thedesire to study density gradientswithin a substance and theirrela~ionship to patterns on thesurface of transparent solids orliquids which also are supposed tohave a flat surface.

The optical layout required tosuperimpose the two types of systemsfor the study of the effect ofconvection on the surface of a liquidwould start with a source slightlyoff the axis of a schlieren fieldlens and one focal length away. Thefield lens projects a paralell beamof ligh~ which is defleoted by afirst surfaoe mirror at an angle ofclose to, but not quite, 90 degreesand onto the surface of the liquid,here shown in idealized form. Sincethe liquid will automatically have alevel, though not nece~sarily flat,surface, it will reflect asubstantial amount of the incidentlight back up towards the field lens.This light will eventually form animage of the source close to it'sreal location. Since the source wasslightly off axis, it's image willalso be a little displaced. If thesurface is truly flat, then at theplane of this image, all the pointson the liquid surface will contributetheir own individual images of thesource. If, however, some surfacepoints are at an angle, then theimages of the source formed by thesepoints will be displaced and willinteract with the knife edge inunequal ways causing a typicalschlieren pattern of light and darktones to appear on the camera'sscreen.

In conclu.ion, while the theory andapplications of shadowqraphs andsohlieren systems seem to have beenexhausted and the processes describedin ;r.at detAil by a great number ofworker5 in this field, I hope thatthe material whioh you have hearddiscussed and seen demonstrated inthis workshop has helped to introduceyou to some of the ba.io conceptsassociated with these oftenmisunderstood techniques. Although Iprobably could not help withmathematical model in; of thesesystem., if I may be of further helpin any other way plaase do nothesitate to write to me at the PhotoTech DepArtment at RIT or simply callme .~ (716)475-2592.

Ignoring for now the liQht that wasreflected at the liquid 9urface, alarge portion of the light incidentOD this $urf~c. passes through intothe bulk of the liquid. ASQuminq thatthe liquid 19 free of densitygradients, the light proceeds down tothe bottom of the containerundisturbed. Here it is reflected byanother first surface mirror alignedat an angle which is not quite 0degrees, which is the ~ngl. th.~ theliquid surface sets itself to. Thelight which is reflected DOW travelsback up through the liquid and out ofthe surface, back through the fieldlens, and eventually ~his light, too,forms .n image of the lighe sourcesomewhere clo•• to the originalsourCE and close to the location ofthe imaoe formed by the liqhtreflected from the surface. A secondknife adoe is inserted into thi.,second, 1mB;e of the source. If thebulk of the liquid has den5ity;radients present, these CAuse theima;e of the source to move withrespect to the second knife edgeoreatin; A schlieren pattern on thescr••n of the second CAmera dueprimarily to the den&ity qradients inthe bulk of the liquid. With someperseverance it is even possible torecord both schlieren patterns on thescreen of a sinole camerA as shown bythe accompanying illustration.

END

IF

......, NOT AT O·