Imaging in fluorescence direct-view microscopy

1 July 1998

Optics Communications 152 Ž1998. 393–402

Full length article

Imaging in fluorescence direct-view microscopy D.T. Fewer, S.J. Hewlett, E.M. McCabe Department of Physics, Trinity College, UniÕersity of Dublin, Dublin 2, Ireland Received 11 November 1997; revised 24 March 1998; accepted 25 March 1998

Abstract We derive a general theory of imaging for the fluorescence direct-view microscope ŽDVM. in terms of the system’s incoherent optical transfer function. Particular attention is given to both the form of the in-focus transfer function and the optical sectioning capability of the instrument in the presence of Ži. a spatially incoherent source and Žii. a spatially coherent Žlaser. source. Unlike its brightfield counterpart, the imaging properties of the fluorescence DVM are shown to be relatively insensitive to the source coherence, provided the pinhole spacing-to-radius ratio is kept sufficiently large. This suggests that the use of a laser source in fluorescence direct-view microscopy could prove to be extremely beneficial as regards increased light throughput and cost-effectiveness. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Confocal microscopy; Direct-view microscopy; Fluorescence imaging; Multiple-pinhole arrays; Source coherence

1. Introduction Confocal fluorescence scanning microscopy is now a well-established technique and an essential tool for obtaining high-contrast images of many biological specimens w1x. The principal advantage of the confocal arrangement is its unique optical sectioning capability which permits a thin slice of material inside a thick specimen to be efficiently imaged. Out-of-focus fluorescence radiation originating away from the focal plane of the lens is greatly attenuated by the confocal detection pinhole w2x. This is in contrast to the conventional non-scanning microscope where, in general, good quality imaging can only be achieved if the sample is thin. The tandem-scanning or direct-view microscope ŽDVM., first developed by Egger and Petran ´ˇ in the late 1960’s w3,4x, possesses many of the advantages of the confocal scanning microscope while retaining the simplicity of the conventional non-scanning microscope. It typically employs a Nipkow disc containing many pinholes arranged as interleaving Archimedean spirals in the source and detector planes. The disc is illuminated by an incoherent light source and rotated such that the sample is probed simultaneously by many points of light which scan the entire field-of-view. This permits real-time inspection of the specimen and is similar to having many confocal microscopes operating in parallel. The DVM has been used to study a diverse range of specimens in both brightfield and fluorescence imaging modes w5–7x. In general, however, it is not primarily suited to low signal level applications because of its extremely poor light throughput: typically only 1–2% of the cross-sectional area of the Nipkow disc is transparent w5x. This very inefficient use of illumination light is even more prevalent in fluorescence direct-view microscopy where the incoherent light source is usually filtered to provide a relatively narrow band of wavelengths spanning the fluorescence excitation peak. Furthermore, the quantum efficiency of fluorescence generation is always less than 100%. For a given optical sectioning requirement, the overall light throughput in both the brightfield and fluorescence DVM can be optimised by tailoring the specific arrangement of pinholes in the Nipkow disc w8–10x. An alternative method of improving the light throughput might be to employ a highly directional input beam from a Žcoherent. laser source with the 0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 1 7 4 - 6

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potential of virtually unlimited power. In general, however, the use of a coherent source in the brightfield DVM has been shown to result in a considerable degradation in the imaging properties w11x. The instrument’s optical sectioning capability, for example, is adversely affected by constructive interference effects which give rise to pronounced side-lobes in the axial response to a plane mirror specimen. It is also important to investigate if a similar degradation in performance is observed in the fluorescence DVM, where the source coherence may prove to be less of a problem due to the spatially incoherent nature of the fluorescence generation process. In this paper we derive, for the first time, a general theory of imaging in the fluorescence DVM via the system’s incoherent optical transfer function. Previous papers have considered only the optical sectioning Žaxial. capability of the instrument and have not addressed the transverse imaging or transfer function of the system. With a view to improving the light throughput of the instrument, Sections 2 and 3 compare the effect of using incoherent and coherent Žlaser. illumination, respectively, on the in-focus optical transfer function. We then turn our attention to the most important feature of the fluorescence DVM – its optical sectioning capability. Section 4 investigates the effect of both the source coherence and the pinhole-array geometry on the axial response to a fluorescent planar object. Our results suggest that, unlike the case of the brightfield DVM, the use of a coherent source in the fluorescence instrument does not, in general, cause a significant degradation in the imaging properties.

2. Fluorescence DVM with an incoherent source and detector In this section, we consider the optical arrangement depicted in Fig. 1 where a transmission system is shown for clarity. The object has a spatial distribution of fluorescence generation f Ž t 0 . and is kept stationary, while the source and detector arrays have intensity sensitivities SŽ t 1 . and DŽ t 2 ., respectively, and are scanned in synchronism. The variable t s denotes the scan position referred to the focal plane of each lens. Illumination of the sample occurs at the primary wavelength, l1, via the objective lens with pupil function P1Ž u1, j 1 . and magnification M. Fluorescence radiation is generated within the object at the secondary wavelength, l2 , and is collected by the collector lens with pupil function P2 Ž u 2 , j 2 . and magnification M. The axial coordinates u1,2 represent defocus, while the lateral coordinates j 1,2 are normalised such that the pupil functions are zero for < j 1,2 < ) 1. Throughout this paper we work in terms of the dimensionless optical coordinates, t and u, in the lateral and axial directions, respectively. These are defined relative to the primary wavelength, l1, and are related to the real transverse distance, r, and real defocus, z, via the expressions w2x: ts

2p n

l1

r sin a

Ž1.

and us

8p n

l1

z sin2

a

ž / 2

.

Ž2.

Here, the parameter n represents refractive index and allows for the use of immersion objectives with numerical aperture n sin a .

Fig. 1. Optical arrangement of the fluorescence DVM for which the theory is developed.

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2.1. Optical transfer function We begin by investigating the imaging properties of the fluorescence DVM via the system’s incoherent optical transfer function. This permits us to make some general remarks about the imaging by decoupling the optical system from the particular object under investigation. Using standard techniques w2x the optical transfer function of the reflection-mode fluorescence DVM may be written as 1: C Ž u, m ˜ .s

H g Ž u, j . g 1

j

u 2

b

, bŽm ˜ y j . FSmD

ž / M

d 2j ,

Ž3.

where the symbols F and m denote the Fourier transform and convolution operations, respectively. The parameter b s l2rl1 represents the wavelength ratio while DŽ t . s DŽyt .. The vector m ˜ s m l1rsin a , where m denotes a spatial frequency in the t-direction, is usually expressed a two orthogonal normalised spatial frequencies, Ž m, ˜ n˜ ., but here we retain ) .Ž m u, j . and assume circularly symmetric ˜ for conciseness. We have also introduced the notation g 1,2Ž u, j . s Ž P1,2 m P1,2 lens pupils throughout such that:

P1,2 Ž u, j 1,2

° ¢0

. s~exp

ž

y

ju < j 1,2 < 2 2

/

< j 1,2 < F 1,

Ž4.

otherwise.

Ref. w12x derives the functional form of g 1,2 Ž u, j . as: g 1,2 Ž u, j . s g 1,2

° ¢0

4

H Ž u, < j < . s~ p u < j <

cosy1 Ž < j
ž


sin u < j < cos u y

0

2

/

cos u d u

< j < F 2,

Ž5.

< j < ) 2,

where we have normalised to unity at < j < s 0. We now consider the general case of an arbitrary source array comprising N identical apertures, each with an intensity distribution S1Ž t ., which are centred on the points T1, T2 , . . . , TN such that: N

SŽ t . s

Ý S1Ž t y T1 . .

Ž6.

is1

The transfer function for the fluorescence DVM employing an identical arrangement of apertures in both the source and detector arrays can then be written as: N

C Ž u,m ˜ .s

N

Ý Ý H g 1Ž u, j . g 2 is1 js1

u

b

j

,b Ž m ˜ y j . FS1mS1

ž / M

exp y

j j P Ž Ti y Tj . M

d 2j .

Ž7.

For a given array of apertures in the source and detector planes, Eq. Ž7. is somewhat unwieldy and is, in general, time consuming to evaluate numerically. It is, however, straightforward to compute the form of the fluorescence DVM transfer function in a number of important limiting cases, as we now discuss. In the limiting case of source and detector arrays comprising a single, infinitely large aperture Ži.e., N s 1 and FS1 Ž j . s d Ž j . in Eq. Ž7., where d denotes the Dirac delta function. the transfer function reduces to the form: C Ž u,m ˜ . s C Ž u, < m˜ < . s g 2

ž

u

b

/

,b < m ˜< .

Ž8.

This is identical to the transfer function of the conventional ŽType I. incoherent scanning microscope w13x operating at the fluorescence wavelength, l2 . We henceforth refer to it as the Type I limit for the fluorescence DVM. It should be noted that because b s l2rl1 ) 1 for most specimens of interest, the spatial frequency cutoff of C Ž u, m ˜ . for the Type I fluorescence DVM Ži.e., < m ˜ < s 2rb . will always be less than its scanning-microscope counterpart, where the resolution is determined solely by the excitation wavelength, l1 w2,14x. The reason for this is that the roles of the collector and objective lenses are

1

For reflection-mode imaging we set u1 s u 2 s u but retain the subscripts on P1,2 for clarity. We also neglect premultiplying constants throughout.

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reversed in the two instruments. A similar role reversal also occurs in the Type I brightfield DVM and its scanning-microscope counterpart w11,15x. At the other extreme when the source and detector arrays comprise a single, infinitely small pinhole Ži.e., N s 1 and FS1Ž j . s 1 in Eq. Ž7.. the transfer function of the confocal ŽType II. fluorescence DVM takes the form: C Ž u,m ˜ . s C Ž u, < m˜ < . s g 1Ž u, < m˜ < . m g 2

ž

u

b

/

,b < m ˜< .

Ž9.

This is identical to the incoherent transfer function derived by Wilson w14x for the confocal ŽType II. fluorescence scanning microscope and has a spatial frequency cutoff < m ˜ < s 2Ž1 q 1rb .. For the intermediate case of a fluorescence DVM whose source and detector arrays comprise a single, finite-sized circular pinhole of normalised radius Õp , we set N s 1 and FS1Ž j . s

2 J1 Ž y p < j < . Õp < j <

Ž 10.

in Eq. Ž7.. Here, J1 denotes the first-order Bessel function of the first kind w16x and we have normalised to unity at Õp s < j < s 0. The normalised pinhole radius, Õp , is related to the actual pinhole radius, r p , via the expression Õp s Ž2p nrl1 . r p sin a . Fig. 2 plots the in-focus optical transfer function in the n˜ s 0 direction, C Ž0, m, ˜ n˜ s 0., for the fluorescence DVM employing a single pinhole of normalised radius Õp in the source and detector planes. Also plotted are the Type I and Type II limits for the fluorescence DVM based on Eqs. Ž8. and Ž9., respectively. As one would expect intuitively, increasing the normalised pinhole radius, Õp , results in a reduction in the number of spatial frequencies passed by the system’s transfer function. The frequency at which the transfer function reduces to 0.1% of its maximum value reduces from m ˜ f 3.3 for Õp s 1.0 optical unit to m˜ f 2.35 for Õp s 12.0 optical units. Therefore, for Õp G 12.0 optical units we would expect the imaging properties of the fluorescence DVM to be similar to that of the conventional fluorescence microscope. In order to get some idea of how the array size influences the fluorescence DVM’s optical transfer function, we consider the limiting case of source and detector arrays comprising infinitely small pinholes Ži.e., FS1Ž j . s 1 in Eq. Ž7... Furthermore, we specialise to the particular case of an n = n square array of pinholes with nearest neighbour spacing R optical units in the source and detector planes. This can be implemented mathematically by specifying a pinhole position vector, Ti s Ž kR, lR ., where k,l s 1, 2, . . . , n w9x in Eq. Ž7.. Fig. 3 compares the form of the infocus optical transfer function in the n˜ s 0 direction, C Ž0, m, ˜ n˜ s 0., for various square array sizes with Ža. R r M s 2 optical units and Žb. R r M s 5 optical units. These pinhole spacings are somewhat smaller than would typically be used in practical DVM systems but are deliberately chosen here to exaggerate the trends. In general, the spatial frequency response of the transfer function degrades as the array size is increased andror the pinhole spacing is decreased. In the case of R r M s 2 optical units the degradation from the Type II to the Type I limit is quite rapid due to the close proximity of the pinholes. Similar trends are also observed for the R r M s 5 case but they are less pronounced due to the larger pinhole spacing. As the pinhole spacing is increased above

Fig. 2. In-focus optical transfer function, C Ž0, m, ˜ ns ˜ 0., for the incoherent-source fluorescence DVM employing single pinholes of normalised radius Õp in the source and detector planes. Also shown are the corresponding Type I and Type II fluorescence DVM transfer functions.

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Fig. 3. In-focus optical transfer function, C Ž0. m, ˜ ns ˜ 0., for the incoherent-source fluorescence DVM employing square n= n arrays of point pinholes with Ža. R r M s 2 and Žb. R r M s 5 optical units. Also shown are the corresponding Type I and Type II fluorescence DVM transfer functions.

R r M s 5 optical units, the sensitivity of the optical transfer function to array size decreases. For example, if we set R r M s 10 optical units, we find that the transfer functions for different array sizes essentially lie on top of each other, close to the Type II limit.

3. Fluorescence DVM with a coherent source and an incoherent detector We now move on to consider the effect of using a spatially and temporally coherent light source in the fluorescence DVM. This, for example, will permit us to predict the imaging properties when laser radiation is used to excite the fluorescence generation within the sample. Compared to the more traditional choice of an incoherent light source, the laser offers a potentially cost-effective means of dramatically improving the light throughput in DVM’s due to its high degree of beam directionality. In a previous paper w11x, we have shown, theoretically, that the confocal imaging characteristics of the brightfield DVM suffer significant degradation in both the lateral and axial direction when a coherent source is employed. However, it is of interest to investigate the effect of a using coherent source on the imaging properties of the fluorescence DVM, where the fluorescence generation is essentially a spatially incoherent process. To this end, we again refer to Fig. 1 and now assume that the source has an amplitude sensitivity SAŽ t 1 . while the detector has an intensity sensitivity DŽ t 2 .. The subscript A is used throughout to explicitly denote an amplitude sensitivity. 3.1. Optical transfer function Using an analogous technique to that adopted in Section 2.1, the incoherent optical transfer function for the coherent-source fluorescence DVM may be derived as: C Ž u,m ˜ .s

Hg

1,eff

Ž u, j . g 2

u

b

j

,b Ž m ˜ y j . FD

ž / M

d 2j .

Ž 11 .

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398

) .Ž ) Ž Here, we have introduced the notation g 1,eff Ž u, j . s Ž P1,eff m P1,eff u, j ., where P1,eff Ž u, j . s P1,eff u,y j .. The effective pupil function, P1,eff Ž u, j ., has also been defined as P1,eff Ž u, j . s FS AŽ jrM . P1Ž u, j .. We first consider the general case of an arbitrary source array comprising N identical apertures, each with an amplitude distribution S1 AŽ t ., which are centred on the points T1, T2 , . . . , TN such that:

N

SA Ž t . s

Ý S1 A Ž t y Ti . .

Ž 12.

is1

The transfer function for the fluorescence DVM employing an identical arrangement of apertures in both the source and detector arrays can then be written as: N

C Ž u,m ˜ .s

Ý H g 1,eff Ž u, j . g 2 js1

u

b

j

,b Ž m ˜ y j . FS1

ž / ž M

exp

j j P Tj M

/

d 2j ,

Ž 13.

N where P1,eff Ž u, j . s FS1 AŽ jrM . P1Ž u, j .Ý is1 expŽyj j P TirM .. As in Section 2.1, we now proceed by computing the form of the optical transfer function for a number of important limiting cases. In the limiting case of a Type I fluorescence DVM employing a single, large-area coherent source and incoherent detector Ži.e., N s 1 and FS Ž j . s FS Ž j . s d Ž j . in Eq. Ž13.., the optical transfer function again reduces to Eq. Ž8. and, as in the 1A 1 case of the incoherent-source fluorescence DVM, the imaging is identical to that of the conventional ŽType I. scanning microscope operating at the fluorescence wavelength. This behaviour is in contrast to the Type I brightfield DVM where the introduction of a coherent source is generally found to degrade the imaging because it significantly reduces the number of spatial frequencies that can be passed by the optical system w11x. At the other extreme, when the source and detector arrays comprise a single, infinitely small pinhole Ži.e., N s 1 and FS1 AŽ j . s FS1Ž j . s 1 in Eq. Ž13.. the optical transfer function again reduces to Eq. Ž9. and, as in the case of the incoherent-source fluorescence DVM, the imaging is identical to the confocal ŽType II. fluorescence scanning microscope. For the intermediate case of a coherent-source fluorescence DVM whose source and detector arrays comprise a single, finite-sized circular pinhole of normalised radius Õp , we set N s 1 and

FS1 AŽ j . s FS1Ž j . s

2 J1 Ž Õ p < j < . Õp < j <

Ž 14.

in Eq. Ž13.. All the exponential terms then cancel. Fig. 4 plots the in-focus optical transfer function in the n˜ s 0 direction, C Ž0, m, ˜ n˜ s 0., for the coherent-source fluorescence DVM employing a single pinhole of normalised radius Õp in the source and detector planes. Also plotted are the Type I and Type II limits for the coherent-source fluorescence DVM based on Eqs. Ž8. and Ž9., respectively. By comparing Figs. 2 and 4 it is evident that the introduction of a coherent source in the fluorescence DVM does not adversely affect the transfer function in terms of its spatial frequency response or cut-off when a single pinhole is employed in the source and detector planes.

Fig. 4. In-focus optical transfer function, C Ž0, m, ˜ ns ˜ 0., for the coherent-source fluorescence DVM employing single pinholes of normalised radius Õp in the source and detector planes. Also shown are the corresponding Type I and Type II fluorescence DVM transfer functions.

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Finally, in the limiting case of a coherent-source fluorescence DVM employing source and detector arrays comprising infinitely small pinholes Ži.e., FS1 AŽ j . s FS1Ž j . s 1 in Eq. Ž13.., the optical transfer function may be readily expressed in the form: N

C Ž u,m ˜ .s

N

Ý H Ý h1 js1

is1

ž

u, t q

Ti y Tj M

2

u

t

/ ž / h2

, b b

2

exp Ž jm ˜ P t . d2 t .

Ž 15 .

Here, the amplitude point-spread function, h1,2 Ž u, t ., is defined via the Fourier transform relationship: h1,2 Ž u, t . s

HP

1,2

Ž u, j . exp Ž yj j P t . d 2j ,

Ž 16.

which, in the absence of defocus, takes the functional form h1,2 Ž u s 0, t . s 2 J1Ž< t <.r< t <. Fig. 5 compares the form of the in-focus optical transfer function in the n˜ s 0 direction, C Ž0, m, ˜ n˜ s 0., for various square array sizes with Ža. R r M s 2 and Žb. R r M s 5 optical units. It is evident that increasing the pinhole spacing from R r M s 2 to R r M s 5 optical units has little effect on the in-focus transfer function. This is in contrast with the incoherent-source fluorescence DVM ŽFig. 3. where a reasonable improvement in the spatial frequency response of the system is observed on increasing the pinhole spacing to R r M s 5 optical units. This suggests that the in-focus image obtained with the coherent-source fluorescence DVM will be less confocal in nature than that of its incoherent-source counterpart when the pinhole spacing is R r M s 5. However, if the pinhole spacing is increased to R r M s 10 optical units, the transfer function for different array sizes essentially lie on top of each other, close to the Type II limit. This is in analogy with the incoherent-source fluorescence DVM. Consequently, we expect that the source coherence will only have a significant effect on the in-focus intensity image of the fluorescence DVM when the pinhole spacing is small.

Fig. 5. In-focus optical transfer function, C Ž0, m, ˜ ns ˜ 0., for the coherent-source fluorescence DVM employing square n= n arrays of point pinholes with Ža. R r M s 2 and Žb. R r M s 5 optical units. Also shown are the corresponding Type I and Type II fluorescence DVM transfer functions.

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4. Optical sectioning strength One of the main reasons for using the fluorescence DVM in biological applications is its inherent ability to obtain real-time images of a thin slice of material within a thick specimen via its optical sectioning capability. For low-light level fluorescence work, however, the confocal ŽType II. scanning microscope has clear advantages in terms of light availability. In a previous paper w9x we have shown theoretically that, by altering the design of the disc, it is possible, in principle, to increase the light throughput in the fluorescence DVM without significantly degrading the optical sectioning characteristics. It is also interesting to ask if one might achieve a similar improvement in light throughput by using a laser source to provide a highly directional input beam with the potential of virtually unlimited power. In this section, we investigate the feasibility of using a spatially and temporally coherent laser source in the fluorescence DVM by considering its effect on the optical sectioning capability of the instrument. To quantify the strength of the optical sectioning, we follow Ref. w17x and monitor the variation in the detected signal as a uniform fluorescent planar object is scanned axially through focus. The theoretical intensity image then becomes a function of defocus only and takes the functional form: I PLANE Ž u . s C Ž u,m ˜ s 0. .

Ž 17.

In the case of a fluorescence DVM employing an incoherent source and detector, the planar axial response may be derived from Eq. Ž7. as w9x: N

I PLANE Ž u . s

N

2r b

Ý Ý H0

g 1Ž u, r . g 2

is1 js1

r

u

ž

b

/ ž / ž

, br FS1mS1

M

J0

r M

< Ti y Tj < r d r ,

/

Ž 18 .

where J0 denotes the zeroth-order Bessel function of the first kind w16x and the individual pinholes, S1Ž t ., are assumed to be circularly symmetric. Similarly, for a fluorescence DVM employing a coherent source and an incoherent detector, Eq. Ž13. yields the planar axial response: N

Ý H < h1,eff Ž u, t . < 2

I PLANE Ž u . s

h2

js1

u

2

t

ž / ,

m S1Ž Mt q Tj . d 2 t ,

b b

Ž 19.

where the individual pinholes, S1 AŽ t . and S1Ž t ., are again assumed to exhibit circular symmetry. Here, by analogy with Eq. Ž16., we have introduced the effective amplitude point-spread function, h1,eff Ž u, t ., via the Fourier transform relationship: h1,eff Ž u, t . s N

s

HP

1,eff

Ž u, j . exp Ž yj j P t . d 2j

r

1

Ý H0 FS

1A

is1

ž / M

ž

P1 Ž u, r . J0 r t q

Ti M

Ž 20.

/

r d r.

Ž 21 .

We also note that for circular pinholes of normalised radius Õp , the convolution function in Eq. Ž19. takes the functional form w18x: h2

u

2

t

ž / ,

m S1Ž Mt q Tj .

b b

°

2p s~

Ž Õ p rM .yr

H0

¢2H

rq Ž Õ p rM .

ry Ž Õ p rM .

u

ž / ž /

h2

h2

2

t

, b b

u

t

, b b

t dtq2

Ž Õ p rM .qr

HŽ Õ rM .yr p

h2

u

t

ž / , b b

2

cosy1 Ž a . t d t

r-

cos

Ž a .t dt

M

,

Ž 22.

2 y1

Õp

rG

Õp M

,

where h 2 Ž u,t . s h 2 Ž u, < t <., r s < t q ŽTjrM .< and a s w r 2 q t 2 y Ž ÕprM . 2 xrŽ2 rt .. Wilson and Hewlett w17x have previously addressed the effect of source coherence on the planar axial response of a fluorescence DVM whose source and detector arrays comprise a single, finite-sized circular pinhole of normalised radius Õp Ži.e., N s 1 and FS Ž r . s FS Ž r . s 2 J1Ž r Õp .rŽ r Õp . Eqs. Ž18. and Ž19.. In general, it was shown that the optical sectioning 1A 1 characteristics are relatively insensitive to the spatial coherence of the source when a single pinhole is employed as source and detector. This is in analogy with the single-pinhole brightfield DVM w17x. In order to get some idea of how the array size influences the fluorescence DVM’s optical sectioning properties, we concentrate on an n = n square array of circular pinholes with an object-plane spacing R r M s 10 optical units and radius Õp r M s 1 optical unit. Fig. 6 compares the theoretical I PLANE Ž u. curves for various square array sizes in the fluorescence DVM employing Ža. an incoherent source and detector and Žb. a coherent source and an incoherent detector. Although the

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Fig. 6. Theoretical I PL ANE Ž u. curves for the fluorescence DVM employing square n= n arrays of circular pinholes with R r M s10 optical units and Õp r M s1 optical unit. Ža. Incoherent source and detector and Žb. coherent-source and incoherent detector. ISINGLE denotes the axial response for a single, finite-sized pinhole with Õp r M s1 optical unit.

half-width at half-maximum values are marginally smaller in the coherent-source responses, it is apparent that, in general, the source coherence has little effect on the fluorescence DVM’s optical sectioning characteristics. This is in contrast to the analogous brightfield DVM responses, where pronounced side-lobes are observed in the presence of a coherent source w11x. The side-lobes arise from constructive interference effects and dramatically reduce the instrument’s optical sectioning capability. It is clear from Fig. 6 that this problem does not occur in the fluorescence DVM due to the spatially incoherent nature of the fluorescence generation process. We note that the background levels in the axial response shown in this Figure would not be easy to predict without the theoretical analysis presented in this paper. In principle, therefore, a coherent laser source could be employed in the illumination path of the fluorescence DVM, without compromising the optical sectioning capability of the instrument. This would be a highly cost-effective means of achieving a significantly higher light throughput for the real-time imaging of biological specimens. It is also advantageous that the peak absorption features in many common dyes are synthetically tailored to correspond to common laser wavelengths. An approach like this would be novel because most commercial DVM systems utilise an incoherent light source.

5. Conclusions In conclusion, we have investigated the effect of both source coherence and pinhole distribution on the imaging properties of the fluorescence DVM. This has been achieved by deriving, for the first time, a general theory of imaging via the system’s incoherent optical transfer function. Some general properties of the imaging have been predicted by considering a number of important limiting pinhole-array configurations. For single-aperture arrays comprising a finite-sized circular pinhole, the spatial coherence of the source was shown to have little effect on the form of the in-focus transfer function. This is in contrast to the case of multiple-pinhole arrays when the pinhole spacing is small: as the array size is increased, the spatial frequency response of the coherent-source DVM

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degrades toward the Type I limit considerably faster than its incoherent-source counterpart. These problems are, however, not predicted to occur in practical fluorescence direct-view microscopy where relatively large pinhole spacings of R r M G 20 optical units are typically employed. Perhaps the most important property of the fluorescence DVM is its unique ability to obtain real-time images with a very narrow depth-of-focus, i.e., its optical sectioning capability. To quantify the influence of source coherence on the three-dimensional imaging characteristics, we have considered the axial response to a perfect planar fluorescent object. It was shown that the spatial coherence of the source has virtually no effect on the ability of the multiple-pinhole fluorescence DVM to discriminate between different depths within a specimen. This is in contrast to the brightfield DVM where the use of a coherent Žlaser. source renders the microscope essentially unusable for depth measurements w11x. In principle, therefore, a laser source could be an extremely beneficial addition to the fluorescence DVM which, to date, has utilised an incoherent light source.

Acknowledgements This research was supported by Forbairt Project No. SCr96r713. DTF is funded by Forbairt and was the recipient of a Trinity College Postgraduate Award. SJH is funded by the European Union under the Human Capital and Mobility Program.

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