Effect of axial pinhole displacementin confocal microscopes

Shigeharu Kimura and Tony Wilson

The effect of axial misalignment of the detector pinhole in confocal microscopes is investigated. We findthat the use of a flat mirror to determine the axial position of the pinhole in a reflection microscope doesnot necessarily give the correct location. However, for a fluorescent microscope there is no uncertaintyin determining the axial position of the pinhole by maximizing the fluorescence signal from a thinfluorescent film.

Introduction

Confocal scanning microscopes employ pinhole orpoint detectors that make them optically superior inmany ways to conventional instruments. The resultof using a pinhole detector is that the resolution inthe lateral direction is superior to that in conven-tional instruments. This can be demonstrated theo-retically by considering the form of either the pointspread functions or transmission cross coefficients(transfer functions).1 The key advantage of the con-focal microscope, of course, concerns its depth discrim-ination property.2

In particular, the depth discrimination capability isimportant since it permits us to observe objects threedimensionally. This capability has been applied, inthe reflection case, to surface profile measurementsand in the fluorescence case to the observations ofbiological structures 4 and lithographed photoresistfilms that are utilized in the production of semiconduc-tor devices.5

The degree of optical sectioning or depth discrimi-nation that is achieved depends on the pinhole size.This dependence has been discussed for both thereflection confocal microscopes and the fluorescentconfocal microscope.7 The smaller the radius of thepinhole, the clearer the superiority. If we use a largepinhole detector, the superiority is lost. It is clearlydesirable to use the smallest pinhole detector that

gives a signal-to-noise ratio that is sufficient to obtaina respectable image.

It is important not only to choose a detector pinholeof the correct size but also to make sure that iscorrectly positioned in the microscope optical system.We describe the effects of axial pinhole displacementin both reflection and fluorescence confocal micro-scopes. We analyze the effects of axial misalignmentby considering the form of the detected signal as wescan either a flat mirror or thin fluorescent sheetthrough focus. The differences between the re-sponses in the two cases suggest that we should becareful when we align microscopes by using a flatmirror.

Axial Response

The two types of confocal microscope that we analyzehave almost exactly the same optical arrangementbut completely different theoretical descriptions.Bright-field reflection imaging is completely coherentwhereas in fluorescence the imaging is incoherent.

We consider axial responses when a flat mirror or athin fluorescent film is the object. The diagram ofthe optical system of a confocal microscope is shownin Fig. 1. Here, assuming unity refractive index, weintroduce the normalized optical coordinates as fol-lows:

S. Kimura is with the Central Research Laboratory, Hitachi,Ltd., Kokubunji, Tokyo 185, Japan; T. Wilson is with the Depart-ment of Engineering Science, University of Oxford, Parks Road,Oxford OX1 3PJ, UK.

Received 2 June 1992.0003-6935/93/132257-05$05.00/0.t 1993 Optical Society of America.

27rv = -x sin 0,

2,rU = - Z sin 2 0,

X

2 1rvy = - y sin 0,

(1)

1 May 1993 / Vol. 32, No. 13 / APPLIED OPTICS 2257

where the pupil has a normalized radius of unity.If the radius of the pinhole aperture is vr, then itstransmittance function is

1 if (vXD2 + v 2)1/2 < V_D(VXD, VYD) = 0 if (VXD2 + VYD2 )1 /2 > , (6)

confocalpoint

Fig. 1. Schematic diagram of a confocal microscope.

2rrVxD = XD sn p,

2Xr . 2

UD -= A ZD sm )x

2 'rr si pVYD = AyD s (P.

(2)

The substitution of Eq. (4) and Eq. (3) permits us towrite

J _ _ h(vx, v,, u + o)

x h(vxD - vx, VyD - Vy, u + UD)dvxdvy

= f' f P1(xo0Yo)P2(xoYo)

x exp[i uo + DU)(XO2+yo2)1

where sin 0 and sin cp are the numerical apertures ofthe lens in the object space and the image space,respectively, is the wavelength of light that isemitted from the point source, and Xo is the wave-length of light that is incident on the optical detectorthrough a pinhole. The origin of the rectangle coor-dinates (x, y, z) is coincident with the Gauss point ofthe point source, and the origin of the rectanglecoordinates (XD, YD, ZD) is also coincident with theGauss point of the other origin. These origins of thecoordinates are assumed to be fixed even if the pointsource is displaced from the original point.

We represent axial displacements of the pointsource and the detector as uo and UD. For thereflection confocal microscope, the wavelength Xo isequal to the source wavelength. In this case if a flatmirror is taken to be the object we can write thevariation in detected signal as

I(U, UOUD) = (2,2 5 5 5 S h(V vxy, u + Uo)

x h(VXD - vx, VyD - Vy, U + UD)

x dvxdvy I 2 D(vXD, VYD) dvXDdVYD, (3)

where h represents the amplitude point spread func-tion and D(VXD, VyD) is the transmittance function ofthe pinhole behind which the optical detector ispositioned. The amplitude point spread functionmay be written as

h(vx, uy, U) = I J P(xo, yo)exp [2 (Xo2 +y0 2)1

x exp[i(vxxo + vyyo)jdxody, (4)

We assume that the circular exit pupil function P(xo,Yo) is

tI if (xo2 + yo2)1/2 < 1P(xo, YO) 0 if (X0

2± y0~2)1/2 > ()

x exp[i(xOvxD + y0vyD)]dxodyo, (7)

where P1 and P2 denote the exit pupil functions of theobject space and the image space, respectively. If weassume that P1 = P2, Eq. (7) takes the form

f f h(vx, vy, u + uo)

x h(vxD - vx, vyD - vy, u + UD)dvXdvy

= 21rh(vxD, vyD, UO + UD + 2U), (8)

by using the symmetry of the circular pupil.fore Eq. (3) can be expressed as

There-

I(U, Uo, d) = J J Ih(vXD, VyD, Uo + UD + 2U)12

x D(vXD, VyD)dVxDdVyD. (9)

If the radius of the pinhole is infinitely small, theintensity variation becomes8' 1

I(U, Uo, Ud) = Ih(0, 0, uo + UD + 2U)I2

_ Isin[(uo + UD + 2)/4] 2(UO + UD + 2U)/4 J (10)

The calculation of the variations when the pinhole isnot vanishingly small is presented elsewhere.6

Equations (9) and (10) suggest that, if the pointsource or point detector are displaced from theircorrect positions, the only effect on the axial responseis to introduce an axial shift. The shape of theirresponse is unaffected. Therefore is we scan a flatmirror through focus and adjust the detector pinholeposition such that we obtain a sinc2 type response wehave no confidence that the pinhole is in the correctposition. If the pinhole is not in the correct axialposition we do not obtain the best lateral resolution

2258 APPLIED OPTICS / Vol. 32, No. 13 / 1 May 1993

confocalpoint

lens

since the effective point spread function woulbroader than it should be.

In order to discuss this deterioration we choodiscuss the form of the coherent transfer fun(C(s, t, U, UD) when the detector pinhole has displaced axially. Here s and t are normalizedtial frequencies in the x andy directions, respectiFor simplicity we assume that Uo = 0. This trarfunction is expressed as

C(s, t; U, UD) = P(s, t)exp[- (S2 + t2)11

0 {P(s, t)exp[2 (U + UD)(S 2 + t2)

where 0 denotes a convolution in the (s, t) donSince we obtained the maximum when the flat miis positioned at = -UD/2, the substitution ofinto Eq. (11) gives

(s -'UDC S,t; 2' UDJ= {P(s t)exp[- UD (S2 + t2)

( P(S, t)exp iU (S2 + t2)

This equation is similar to the optical transfer ftion of an incoherent conventional defocused opsystem9 and therefore this transfer function of(12) is always lower than that of UD = O. Incideily, if the condition that o + UD = 0 is satisfied in(9) or Eq. (10), the variation is the same as that olconfocal point. However, note that the real confpoint should satisfy the condition that Uo = UD.

The effective point spread function of the confbright-field microscope is given by the product ofpoint spread functions of the two imaging len.If we take o = 0 we can write the effective pspread function, heff, as

heff = h(u, y)h(u + UD, V),

where v is a radial coordinate. At the o = -zposition of the maximum signal from the flat mithe effective point spread function becomes

I be

se toctionbeenspa-vely.isfer

II,

0.05

t0.04

t 0.03

E 0.02

0 2 4 6 8 10 12

Fig. 2. Axial responses of the confocal fluorescent microscopewith a pinhole of vr = 0. The axial displacement of the pinholeranges from UD = 0 to 12.

(11) ~effect on the measured axial response is the introduc-tion of an axial shift. Hence this method cannot be

iain. used to locate accurately the detector pinhole relativerror to the source pinhole. The maximum intensity oc-this curs when the mirror is halfway between the loca-

tions of the images of the source and detector pin-holes in the object space, that is, when the source isimaged onto the detector pinhole. The area of themirror that is illuminated effectively determines thelateral resolution. Thus if the images of the sourceand detector do not coincide in the object space theresolution will deteriorate.

We now turn our attention to the fluorescence case(12) and consider the axial response as an infinitely thin

fluorescent sheet is scanned through focus. If theLlu~nc fluorescence is emitted at a wavelength Xo = MX, theECq intensity variation If (u, o, UD) can be written as7

ital- If (U, UO, UD)l Eq.'thefocal

focalthe

3ses.1

oint

(13)

ZD/2rror

Ih(v., , U + Uo) 12

x h(VxD - VYD - ' + UD)

X D(VXD, vyD)dvXdvydvxDdvyD. (15)

For simplicity in the following we assume that f3 = 1.Calculations made by using Eq. (15) show a shift inthe position of the peak detected intensity and also achange in peak intensity. Figures 2 and 3 show the

1.0

heff h v) (14)

which is wholly real despite the pinhole misalignment.The form of this function is well known and may befound, for example, in Ref. 8, p. 440.

This behavior can be explained by a simple physicalargument. Axial scanning of the plane mirror hasthe effect of axially scanning the apparent imagelocation of the point source in the detector plane.Thus, no matter what the relative displacement isbetween the source and detector positions the only

'm 0.8

X 0.6

z0.4

0.2

6 8 10 220

Fig. 3. Axial responses of the confocal fluorescent microscopewith a pinhole of Vr = 4. The axial displacement of the pinholeranges from UD = 0 to 12.

1 May 1993 / Vol. 32, No. 13 / APPLIED OPTICS 2259

1

(27r)2

intensity variations for pinhole radii vr = 0 and 4,respectively. The parameter of these figures is theaxial displacement of the pinhole ranging from UD = 0to 12. The method of calculation follows that of Ref.7. As the displacement of the pinhole becomes larger,the peak height, which shifts, becomes smaller.Figure 4 shows the peak height normalized by thevalue at UD = 0 for several radii of the pinholeaperture. Since the point spread function I h 12 is aneven function in , it might be assumed that thefluorescence peak takes place at u = -UD/2. IfH(UD) represents the peak height normalized by thevalue at UD = 0, it is expressed as

If (UD/2, 0, UD)- If(0, 0, UD)

1 r~t r~m r~r r+X I {UD 12

If(0, 0, UD) L L f f hVvx V 2

X h(VxD- V VYD- VY Vy )

x D(VXD, vyD)dvxdvydvxDdvyD. (16)

This equation means that the normalized peak heighthas a variation similar to the intensity expressed byEq. (15) except that the width is half as wide as that ofEq. (15).

In order to align the pinhole into the correctconfocal position, we used a thin flat fluorescent filmscanned axially as mentioned above and moved thepinhole axially. Figure 4 suggests that the trueconfocal position is realized at the maximum fluores-cence detected. Therefore seeking the position ofmaximum fluorescence can lead to the true confocalposition. This is fundamentally different from thereflection case. We can understand this by realizingthat in the incoherent fluorescent case the effectiveobject will only be a point when the screen is posi-tioned in the image plane of the source. For anyother location the effective source becomes the defo-

1.0

0.8 6

0.6

0.4 vr O

0.2

0.00 5 10 15

UD

Fig. 4. Variations of the normalized peak height for axial displace-ment of the pinhole in the confocal fluorescent microscope withpinhole radii as parameters. The peak height was obtained whena fluorescent sheet was axially scanned.

6

0 2 4 6 8

UD

10 12

Fig. 5. HWHM of the axial response for displacement of thepinhole for a variety of normalized pinhole radii.

cused intensity point spread function of the lens.In this case it is clear that the peak intensity that canbe measured is reduced since the energy is spreadover a larger spot. In this case then, unlike bright-field reflection imaging, the correct axial alignmentposition can be found by maximizing the detectedsignal.

Figure 5 shows the dependence of the variations ofthe half-width at half-maximum (HWHM) on theaxial pinhole displacement. As the pinhole radiusbecomes larger, the HWHM becomes large. On theother hand, as the displacement becomes large, theHWHM for one radius becomes a little narrower.

Experimental

Figure 6 shows the axial responses of the reflectionthat were obtained by axially scanning a mirrorthrough focus for three axial positions of the confocalpinhole. In the experiment the point source emittedlight at 633-nm wavelength and the pinhole radiuswas 1.5 optical units. The middle curve of the threecorresponds to the pinhole position for true confocaloperation, the right-hand side curve has an axialpinhole displacement of UD = 5.8, and the left-handside trace corresponds to UD = -5.8. The maximumheights of these curves are almost the same as the

Fig. 6. Axial responses obtained from the confocal reflectionmicroscope with an axially scanning mirror. The right-hand sidecurve has a pinhole displacement of UD = 5.8, the left-hand sidecurve represents UD = -5.8, and the middle curve is the confocalpoint.

2260 APPLIED OPTICS / Vol. 32, No. 13 / 1 May 1993

vr=6

Vr2

Vr=

Fig. 7. Axial responses obtained from the confocal fluorescentmicroscope with an axially scanning fluorescent sheet. The right-hand side curve has a pinhole displacement of UD = 6.0, theleft-hand side curve represents UD = -6.0, and the middle curve isthe confocal point.

middle curve in spite of the pinhole displacement.The mirror scanned a total distance of 25 opticalunits. If we refer to the abscissa as the axis of u, thedisplacement of the variations in Fig. 6 is 2.9.According to Eq. (10), the amount of the peak shift ishalf as much as the displacement of the pinhole.Therefore this peak shift agrees with the theoreticalprediction.

Next, instead of the mirror, we used a thin photore-sist film (AZ1400) of 2.7-pum thickness on a glasssubstrate that was scanned in the optical axis direc-tion. Here we used an argon-ion laser of 488-nmwavelength that induces fluorescence with an inten-sity peak of 610 nm from the photoresist. Thepinhole radius used was 4.8 optical units. Threeaxial intensity variations of the fluorescence areshown in Fig. 7. These were obtained after theintensity decrease caused by photobleaching had al-most stopped. The pinhole for the middle curve isset in the confocal position, but the others have axialdisplacements of 6.0 optical units. As shown inFigs. 2 and 3, the amount of the shift of the peakscaused by the displacement of the pinhole is approxi-mately half as much as the displacement. Since onedivision of the abscissa is calculated to be 3.2 opticalunits, the amounts of the peak shifts in Fig. 7 aremeasured to be approximately ±3.2. The reasonthis value is larger than three may be attributed tothe effect of f3 in Eq. (15). In addition, as weexpected, the peak heights become lower when theposition of the pinhole axially departs from theconfocal point, which is different from the reflectioncase of Fig. 6.

Conclusion

Confocal scanning microscopes have depth discrimina-tion capabilities and higher resolution than conven-

tional instruments. These properties are attributedto the pinhole in front of the optical detector in theconfocal microscope. Setting the pinhole at the cor-rect confocal point is important in achieving theseimprovements.

Axial responses with pinhole displacement wereinvestigated for reflection-type and fluorescent-typeconfocal microscopes. We elected to use a flat mirrorand a fluorescent film as objects that were scannedaxially because they are often used to align thepinhole. The pinhole position at which the maxi-mum reflection signal from the flat mirror is obtaineddoes not necessarily correspond to the confocal point.In other words, the best resolution in the lateraldirection is not always attained. Therefore it ispreferable to use an object that has good surfacecontrast to align the pinhole so that maximum con-trast in the image is obtained. On the other hand,moving the pinhole axially to the position at whichthe fluorescence through the pinhole becomes themaximum gives the correct confocal point in thefluorescent confocal microscope.

We thank S. J. Hewlett for many helpful discus-sions. This research was carried out in cooperationwith Hitachi, Ltd.

References

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3. D. K. Hamilton and T. Wilson, "Surface profile measurementusing the confocal microscope," J. Appl. Phys. 53, 5320-5322(1982).

4. R. W. Wijnaendts van Resandt, H. J. B. Marsman, R. Kaplan, J.Davoust, E. H. K. Stelzer, and R. Stricker, "Optical fluorescencemicroscopy in three dimensions: microtomoscopy," J. Microsc.(Oxford) 138, 29-34 (1984).

5. S. Kimura and C. Munakata, "Depth resolution of the fluores-cent confocal scanning optical microscope," Appl. Opt. 29,489-494 (1990).

6. T. Wison and A. R. Carlini, "Size of the detector in confocalimaging systems," Opt. Lett. 12, 227-229 (1987).

7. T. Wilson, "Optical sectioning in confocal fluorescent micro-scopes," J. Microsc. (Oxford) 154, 143-156 (1988).

8. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,1980).

9. H. H. Hopkins, "The frequency response of a defocused opticalsystem," Proc. R. Soc. London Ser. A 231, 91-103 (1955).

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