Wilson Confocal

Confocal scanning optical microscope using single-modefiber for signal detection

Shigeharu Kimura and Tony Wilson

A single-mode fiber is employed as a detector in a confocal scanning optical microscope (CSOM) instead of apinhole and its optical property is studied. The optical system is always coherent, which is fundamentallydifferent from the CSOM with a finite-sized pinhole. The coherent transfer function and the axial responseare calculated. Experimentally, the coherent image is taken and the axial response is also measured.

1. Introduction

The unique imaging properties of the confocal scan-ning optical microscope arise from the use of a pointdetector.1-3 This results in a bright field coherentoptical system whose effective point spread function isgiven by the product of the point spread functions ofthe two imaging lenses. This enhanced effective pointspread function leads to improved imaging and also aunique depth discrimination or optical sectioningproperty which permits thick specimens to be imagedin three dimensions. It is clear that the point detectoris the key element in the confocal system and this isusually realized by placing a small pinhole in front ofthe photodetector. The choice of suitable pinhole sizeand shape has been discussed elsewhere both for brightfield and fluorescence imaging.48 The main conclu-sions are that the lateral resolution improvement ismuch more sensitive to pinhole size than the axialresolution. In the bright field case the use of a finitesized detector results in partially coherent imagingwhich, among other things, makes detailed analysis ofimage resolution difficult. In fluorescence, the imag-ing always remains incoherent.

In certain cases, however, it may be advantageous touse a different form of detector. In spectroscopic im-aging, for example, the optical fiber is a convenientdetector. In the following, therefore, we consider the

role of a single-mode optical fiber as a detector in ascanning microscope. It is clear from geometrical op-tics considerations that we would expect changing thenumerical aperture of the fiber launching lens to besimilar in effect to changing the pinhole radius. How-ever there is a significant difference since the single-mode fiber acts as a coherent detector. The detectedfield is given by an overlap integral between the field atthe fiber face and the mode pattern. This ensures thatthe imaging is always coherent irrespective of the fiberdimensions if the modes can be separated from eachother. This also gives the possibility of performingcoherent signal processing at the same time as signaldetection.

We now discuss the form of the coherent transferfunction and axial response of scanning microscopesusing single-mode optical fibers as a detector. We notonly concentrate on bright field imaging but also showthat analogous remarks may be made in the fluores-cence case.

11. Confocal Microscopy with Single-Mode FiberDetector

We consider the optical arrangement of Fig. 1 wherethe detector is replaced by an optical fiber. Fieldamplitude Uat the endface of the fiber may be expand-ed in terms of a complete set of eigenfunctions ep as9

U = ap ep,

Shigeharu Kimura is with Hitachi, Ltd., Central Research Lab-oratory, Kokubunji, Tokyo 185, Japan, and T. Wilson is with Univer-sity of Oxford, Department of Engineering Science, Parks Road,Oxford OX1 3PJ, U.K.

Received 21 August 1990.0003-6935/91/162143-08$05.00/0.© 1991 Optical Society of America.

(1)

where ap is the excitation efficiency of the pth mode.If we detect the intensity of the pth mode through thefiber, we essentially measure lapt2. In our case we areonly interested in the case of the fundamental modeand hence can write the detected intensity as10

(2)

1 June 1991 / Vol. 30, No. 16 / APPLIED OPTICS 2143

+ + 2I = 1a,1' =if., CU-ejdS1,

detector

Fig. 1. Schematic diagram of the confocal scan-ning optical microscope with single-mode optical

fiber.

where the integral is performed over the entranceplane of the fiber.

It is now a straightforward exercise in Fourier op-tics2' 3'11 to write an expression for the field at theentrance plane of the fiber as

U(tSswstdswd) = j J h(t,,w,)t(t - ton, -woh2

X (to -td,WO - Wd)dtodwo, (3)

where h1 and h2 are the amplitude point spread func-tions of the two imaging lenses and t represents theamplitude reflection or transmittance of the object.The coordinates to and wo represent normalized opticalcoordinates in the object plane. The coordinates t,,w,denote the normalized scan position. The normalizedt coordinates are related to real x coordinates via

t = A. xsina, (4)

where X is the wavelength, sina is the numerical aper-ture, and we have assumed unity refractive index. Asimilar expression related the w coordinate to y. Tofacilitate further calculations, it is convenient to definethe optical coordinates in detector planes td and Wd,

with respect to the numerical aperture sink, as

td =2A Xd siny d =2 Yd sin:. (5)

If we now write the eigenfunction of the fundamen-tal mode as el(td,wd), the total detected amplitude isgiven by

ai(t,,w 8) = j : j L h1(t,,wo)t(t, - to,w - w)ocf . . n c

X h2 (t0 - td,Wo - d)el(td,d)dtOdwodtddwd, (6)

where the optical fiber is clearly behaving as a coherentamplitude detector of sensitivity el(td,wd). Alterna-tively we can introduce an effective point spread func-tion h2eff(tOWO), given by

h2 eff(tOWO) = I | h2 (t0 - td,WO - Wd)el(tdWd)dtddWd, (7)

which permits us to write the image intensity as

I = Ihlelf 0 tl', (8)

where the @ denotes the convolution operation. Thisexpression is identical to that describing the operationof an ideal confocal microscope with a vanishinglysmall point detector except that the point spread func-tion h2 is replaced by h2eff. Alternatively we can de-scribe the system in terms of an effective pupil func-tion. Recalling that the point spread function is given,essentially, by the Fourier transform of the pupil func-tion of the objective, we can write the effective pupilfunction P2eff from Eq. (7) as

P2eff = P2 - E1, (9)

where P2 is the pupil function of the objective lens andE1 is the Fourier transform of e1 . Thus the effect ofthe coherent detector may be thought of as introducingan effective filter of amplitude transmittance E1.12

Thus the question as to how closely a scanning micro-scope with an optical fiber detector resembles a trueconfocal microscope with a point detector may be an-swered by discussing how E1 varies over the extent ofpupil P2. Ideally we would like it to be constant.

Expressions for e1 and E1 are readily available in theliterature1 l'1 3 and in normalized coordinates we maywrite

[vpJ 1(vcp) - Jo(vcp)G(U)]P2eff(P) [(V p)2

- U2 ][(v.p)2 + 2 (0 <p < 1), (10)

where p is the normalized radius of the objective lensand v, is the normalized radius of the core of opticalfiber r, via

VC = A r, sin#, (11)

Jo and Ji are zero- and first-order Bessel functions ofthe first kind, and the function G(U) is given by

UJ1(U)

G(U) Jol)) (12)

When vcp = U, Eq. (10) may be simplified to

2144 APPLIED OPTICS / Vol. 30, No. 16 / 1 June 1991

pointsource

lens

P m

ion affected by the fiber. The (a)waveguide parameter V is 2.4.

10

P2eff(P) J(U) ] }_'2efP 2V2 I (13)

where V2 = U2 + W2 and V = (2ir/X)rcno sinG0 , where nosinG0 is the numerical aperture of the fiber. The termsU and W are modal parameters of the fiber core andcladding, respectively, and may be found as solutionsof the appropriate transcendental boundary conditionequations. Alternatively, they may be convenientlyfound by consulting the table of solutions for specifiedvalues of V in Snyder and Love.13

If we now specialize to the value of V = 2.4 whichalmost corresponds to the limit of single-mode opera-tion, we find that (Ref. 13, page 314) U = 1.645 and W= 1.748. Figure 2 shows the effect on the effectivepupil function of varying v,. In practice this mightcorrespond to changing sin3. It is clear that we re-quire v, to be as small as possible. This corresponds toa sharply peaked eigenmode which will correspondclosely to the ideal confocal point detector.

We can also see this effect by considering the form ofthe coherent transfer function which is given2 from Eq.(8) by

c(m) = P1 0 P2 eff(m), (14)

where m is a spatial frequency. The effect of defocusmay be simply introduced via a phase factor expl/2jup 2 , where u is a normalized axial distance related toreal distance' 4 z via

= Ar z Sin2(a). (15)

Figure 3 shows the results for two values of V, one faraway from cutoff, and in both cases we find that a small

c(m)

0-5

00 1 2

m

(b)

Fig. 3. Coherent transfer functions for the CSOM with the fiber:(a) waveguide parameter V is 2.4 and the normalized radius v, isaltered for each variation; (b) waveguide parameter Vis 1.45 and the

normalized radius vc is altered for each variation.

value of v, is required to give confocal behavior. As vcbecomes larger the apodization is such (see Fig. 2) thatP2eff becomes small and the system behaves like aconventional coherent microscope.

To confirm these predictions a single-mode fiberwith waveguide parameter V = 1.45 was incorporated


Fig. 2. Variations of pupil fund

IH 50gum1 ( -a

(a)

50gtm

(b)Fig. 4. Images usingthe CSOM with (a) the fiber of V =1.45 and (b)

a pinhole radius of 10 ym. The lens numerical aperture is 0.02.

into a scanning optical microscope working with He-Ne laser light (0.6328-,um wavelength). The micro-scope also employed a second 10-,gm diam pinholedetector so that traditional confocal images could beobtained simultaneously. Figure 4 shows comparisonimages where the single-mode fiber image [Fig. 4(a)]was taken with sing = 0.02 corresponding to v, = 0.31.

50pm

Fig. 5. Coherent image by the CSOM using a lens of 0.65 numericalaperture. The waveguide parameter V is 1.45.

Our previous analysis has suggested that this value issufficiently small to give good confocal behavior. Assink and v, are increased, we essentially have a largerarea coherent detector and the imaging changes to thatassociated with conventional coherent imaging. Fig-ure 5 shows the image corresponding to v = 11.3. Thisbehavior is completely different from the incoherentdetector case. We emphasize this by comparing aconfocal image [Fig. 6(a)] with a conventional scanningmicroscope image, i.e., without any limiting pinholeplaced in front of the photodetector [Fig. 6(b)].

I11. Axial Response

We elect to discuss this in terms of the variation indetected signal as a perfect planar reflector is scannedaxially through focus. This axial response is givenby2 ' 3

I(u) = Ic(0)12 = J Pl(p)P 2 eff()pdpI, (16)

which in the case of a perfect point detector confocalmicroscope is given by

21(U) = (17)

The response in the fiber detector case is more compli-cated and is shown in Fig. 7(a) for the case of V = 2.4.These curves are un-normalized and show that themaximum signal is detected when the reflector lies inthe focal plane and v, = 2.1. If we normalize all thesecurves [Fig. 7(b)] we find that, as we might expect, the


1*0

I(u)

0.5

0

H.0 50gum

(a)

1-0

I(u)

0.5

I

050gtm

(b)Fig. 6. Images using the scanning microscope with (a) a 10-,umpinhole (confocal) and (b) a large area detector (conventional). 'The

specimen is the same as in Fig. 3.

smaller the value of v,, the closer the behavior is to trueconfocal.

The question of detected signal level is further dis-cussed in Fig. 8 where we plot the variation of thedetected signal when the reflector lies in the focalplane, I(u = 0), against v for a variety of practical

0

U

(a)

5 10 15U

20

(b)

Fig. 7. (a) Relative axial responses for the CSOM with the wave-guide parameter V = 2.4. The normalized radius is altered. (b)

Axial responses normalized by the values at u = 0.

values of V.15 Each of the curves is normalized to itsmaximum value and show that the value of v, at thehighest launching efficiency becomes small as thewaveguide parameter V becomes small. We plot inFig. 9 the axial response for two values of V where thevalue of v, has been chosen to maximize the launching


on!

l

0 I

0 1 2 3 4 5VC

Fig. 8. Launching power dependence of the CSOM with the fiber

on the normalized core radius. The waveguide parameter V ischanged from 1.05 to 2.4.

1-0

I (u)

0*5

00 10

U

Fig. 9. Axial responses for the CSOM maximizing the launchingpower. The waveguide parameters used for the calculation are 1.05and 2.4, respectively. The dotted line is for the case of a small

pinhole.

efficiency. Thus we do not achieve so great a degree ofoptical sectioning. We show, for completeness, theform of in-focus point spread function, Ih2h2effI2 in Fig.10 for the case of maximum power transfer and againsee that we sacrifice an amount of performance forincreased signal strength.

C0

Ziat

C

0-

4V

Fig. 10. Point spread functions for the CSOM maximizing thelaunching power. The waveguide parameters used for the calcula-tion are 1.05 and 2.4 and both gave results indistinguishable from the

full line. The dotted line is for the case of a small pinhole.

1-0

ZU

0~

a0a;

,

E0z

0-25sin

Fig. 11. Launching power variation against the numerical apertureof the lens of the CSOM. The waveguide parameter V used for the

calculation is 1.45.

Experiments were carried out to confirm these pre-dictions with several lenses of different numerical ap-erture. Figure 11 shows the variation in detected sig-nal as sing is varied and the planar reflector remains inthe focal plane. These results were obtained from anoptical fiber whose waveguide parameter was V = 1.45.


1-0

I (u)

0-5

00 5 10 15 20

U

Fig. 13. Simulations for axial response measurements.

ture case but the difference is not great. Figure 13shows the theoretical predictions for these values ofnumerical apertures and we see that the measuredcurves in Figs. 12(a) and (b) agree almost exactly withthese predictions but that the response of Fig. 12(c) iswider than we might have expected. This may well bethe result of aberrations in the system.

IV. Fluorescence Imaging

All our discussion so far has been concerned withbright field imaging but a fiber detector may be usedequally well in fluorescence imaging. In this case it isstraightforward to write the incoherent image forma-tion process as

I = Ih2efthl12 f, (18)

(C)Fig. 12. Axial responses measured for the CSOM with a waveguideparameter of 1.45. The lens numerical aperture is (a) 0.02, (b) 0.07,and (c) 0.1. Each photograph also shows the narrower responses for

a small pinhole.

Figures 12(a), (b), and (c) show the measured axialresponse for values of sink of 0.02, 0.07, and 0.1, respec-tively. In all cases the response from a pinhole detec-tor is also shown. The horizontal scale of one divisioncorresponds to an axial scan of 1 rim. The pinholeresponse is slightly superior in the 0.02 numerical aper-

where f denotes the fluorescence generation functionand h2,ff is given by Eq. (7). This implies that we canagain think of the system as behaving like a true confo-cal microscope but with a modified second pupil func-tion. The modification is shown in Fig. 2 and again wewould expect good fluorescence images to result with asuitable choice of v. We note, finally, that in the caseof a finite sized incoherent detector D, h2eff is given byIh212 0 D.

V. Conclusion

We have discussed the use of an optical fiber as adetector in a scanning optical microscope and haveshown that it can give identical images to the tradition-al confocal microscope employing a pinhole detector.This may be particularly useful in spectroscopic imag-ing such as Raman microscopy where the fiber canprovide a convenient detector both from the point ofview of the image formation and the input to a spec-trometer.


(a)

Cb)

As the detection is essentially coherent, the imageformation for nonideally sized fiber is fundamentallydifferent from that obtained in traditional systemswith larger than ideal pinhole detectors. In this lattercase the imaging is partially coherent.4 5 We shouldalso mention that we have only considered single-modefibers in this paper. However, if we operate with mul-timode fibers, we can, in principle, choose to detect anyof the modes and hence perform optical coherent sig-nal processing on the image as it is detected. As anexample, detecting the first-order mode will result indifferentiation of the field.

We have also chosen to discuss the case of a pointsource and optical fiber detector. It is straightforwardto extend the analysis to include an optical fiber asboth the source and detector. In this case hi in Eq. (8)is replaced by hleff, where hieff is given by an expressionanalogous to Eq. (7).

We would like to thank S. J. Hewlett for many help-ful discussions.

References

1. M. Minsky, Microscopy Apparatus, U.S. Patent 3,013,467 (19Dec. 1961) (filed 7 Nov. 1957).

2. T. Wilson and C. Sheppard, Theory and Practice of ScanningMicroscopy (Academic, London, 1984).

3. T. Wilson, Ed., ConfocalMicroscopy (Academic, London,1990).4. T. Wilson and A. R. Carlini, "Size of the Detector in Confocal

Imaging Systems," Opt. Lett. 12, 227-229 (1987).5. T. Wilson and A. R. Carlini, "Three-Dimensional Imaging in

Confocal Imaging Systems with Finite Sized Detector," J. Mi-crosc. (Oxford) 149,51-66 (1988).

6. S. Kimura and C. Munakata, "Dependence of 3-D OpticalTransfer Functions on the Pinhole Radius in a FluorescentConfocal Optical Microscope," Appl. Opt. 29,3007-3011 (1990).

7. T. Wilson, "Optical Sectioning in Confocal Fluorescent Micros-copes," J. Microsc. (Oxford) 154, 143-156 (1989).

8. S. Kimura and C. Munakata, "Three-Dimensional OpticalTransfer Function for the Fluorescent Scanning Optical Micro-scope with a Slit," Appl. Opt. 29, 1004-1007 (1990).

9. A. W. Synder, "Excitation and Scattering of Modes on a Dielec-tric or Optical Fiber," IEEE, Trans. Microwave Theory Tech.MTT-17, 1138-1144 (1969).

10. K. F. Barrell and C. Pask, "Optical Fibre Excitation by Lenses,"Opt. Acta 26, 91-108 (1979).

11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill,New York, 1986).

12. T. Wilson and S. J. Hewlett, "Coherent Detection in ScanningMicroscopes," Inst. Phys. Conf. Ser. 98, 629-632 (1990).

13. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chap-man & Hall, London, 1983).

14. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,1975).

15. A. W. Snyder, "Understanding Monomode Optical Fibers,"Proc. IEEE 69, 6-13 (1981).


Documents

Wilson Confocal