KOEHLER INTEGRATOR DEVICE AND APPLICATION THEREOF IN A MULTI-FOCAL CONFOCAL MICROSCOPE

Abstract

A Koehler integrator device (10) comprises a collimating lens (11) being arranged for collimating a light field created by an incoherent or partially coherent light source, a pair of planar first and second micro-lens arrays (12, 13) being arranged for relaying portions of the collimated light field along separate imaging channels, wherein all micro-lenses of the first and second micro-lens arrays (12, 13) have an equal micro-lens focal length and pitch and the micro-lens arrays (12, 13) are arranged with a mutual distance equal to the micro-lens focal length, and a collecting Fourier lens (4) having a Fourier lens diameter and a Fourier lens focal length defining a Fourier lens front focal plane and a Fourier lens back focal plane, wherein the Fourier lens (14) is arranged for superimposing light from all imaging channels in the Fourier lens front focal plane and wherein the second micro-lens array (13) is arranged in the Fourier lens back focal plane, wherein a third micro-lens array (15) is arranged in the Fourier lens front focal plane for creating a wavelength independent array of illumination spots. Furthermore, a confocal microscope apparatus, which comprises the Koehler integrator device, and a method of using the confocal microscope apparatus are described.

Claims

1. A Koehler integrator device, comprising a collimating lens being arranged for collimating a light field created by a light source device to provide a collimated light field, a pair of planar first and second micro-lens arrays, being arranged for relaying portions of the collimated light field along separate imaging channels, wherein all micro-lenses of the first and second micro-lens arrays have an equal micro-lens focal length and pitch and the micro-lens arrays are arranged with a mutual distance equal to the micro-lens focal length, a collecting Fourier lens having a Fourier lens diameter and a Fourier lens focal length defining a Fourier lens front focal plane and a Fourier lens back focal plane, wherein the Fourier lens is arranged for superimposing light from all imaging channels in the Fourier lens front focal plane and wherein the second micro-lens array is arranged in the Fourier lens back focal plane, and a third micro-lens array being arranged in the Fourier lens front focal plane for creating a wavelength independent array of illumination spots.

2. The Koehler integrator device according to claim 1, wherein the third micro-lens array has a pitch in a range from 50 μm to 1500 μm.

3. The Koehler integrator device according to claim 1, wherein the third micro-lens array comprises at least 5*5 micro-lenses.

4. The Koehler integrator device according to claim 1, wherein the third micro-lens array is fixed.

5. The Koehler integrator device according to claim 1, wherein the third micro-lens array is scannable.

6. The Koehler integrator device according to claim 1, wherein each of the first and second micro-lens arrays have a common a pitch in a range from 50 μm to 1500 μm.

7. The Koehler integrator device according to claim 1, wherein each of the first and second micro-lens arrays comprises at least 5*5 micro-lenses.

8. The Koehler integrator device according to claim 1, further comprising a beam sizing optic being arranged between the collimating lens and the first microlens array for changing a diameter of the collimated light field.

9. The Koehler integrator device according to claim 8, wherein the beam sizing optic is arranged for contracting the diameter of the collimated light field and comprises a first beam de-expander lens having a first beam de-expander lens focal length and a second beam de-expander lens having a second beam de-expander lens focal length, which is smaller than the first beam de-expander lens focal length.

10. The Koehler integrator device according to claim 8, wherein the beam sizing optic comprises a variable beam expander.

11. The Koehler integrator device according to claim 8, wherein the beam sizing optic is arranged for expanding the diameter of the collimated light field and comprises a first beam expander lens having a first beam expander lens focal length and a second beam expander lens having a second beam expander lens focal length, which is larger than the first beam expander lens focal length.

12. The Koehler integrator device according to claim 8, wherein the beam sizing optic is adjustable for controlling the diameter of the collimated light field.

13. The Koehler integrator device according to claim 1, further comprising a hard aperture being arranged between the collimating lens and the first micro-lens array for limiting a diameter of the collimated light field.

14. The Koehler integrator device according to claim 13, wherein the hard aperture comprises an iris diaphragm.

15. The Koehler integrator device according to claim 1, further comprising a pinhole array being arranged in a front focal plane of the third micro-lens array for limiting the diameter of generated illumination spots.

16. A method of using a Koehler integrator device according to claim 1, said method comprising creating a pattern of illumination spots in a multi-focal confocal microscope.

17. A confocal microscope apparatus, being arranged for multi-focal sample illumination, comprising a light source device being arranged for creating an excitation light field, a Koehler integrator device according to claim 1, being arranged for creating the array of excitation spots, a scanning device being arranged for creating a scanning pattern of the excitation spots, a focusing optic for focusing the scanning pattern of the excitation spots to a sample to be imaged, and a detector device being arranged for detecting a pattern of emission spots excited by the pattern of excitation spots.

18. The confocal microscope apparatus according to claim 17, wherein the light source device comprises a coherent light source, and a focusing lens and a light scrambling device are arranged between the coherent light source and the collimating lens of the Koehler integrator device.

19. The confocal microscope apparatus according to claim 18, wherein the focusing lens and the collimating lens provide a imaging optic including the light scrambling device.

20. The confocal microscope apparatus according to claim 17, wherein the light source device comprises an incoherent light source.

21. The confocal microscope apparatus according to claim 17, further comprising a pinhole array being arranged in a front focal plane of the third micro-lens array for limiting a diameter of the generated excitation spots.

22. A method of using a confocal microscope apparatus according to claim 17, said method comprising imaging a sample to be investigated.

23. The method according to claim 22, wherein the Koehler integrator device includes a bean sizing optic arranged between the collimating lens and the first micro-lens array for changing a diameter of the collimated light field, wherein the beam sizing optic is arranged for contracting the diameter of the collimated light field and comprises a first beam de-expander lens having a first beam de-expander lens focal length and a second beam de-expander lens having a second beam de-expander lens focal length, which is smaller than the first beam de-expander lens focal length, and the method comprises the step of controlling the diameter of the collimated excitation light field by adjusting the beam sizing optic such that both of a homogeneity of the illumination and a spot size of the excitation spots are sufficient for the imaging of the sample to be investigated.

24. The method according to claim 22, wherein the Koehler integrator device includes a hard aperture arranged between the collimating lens and the first micro-lens array for limiting a diameter of the collimated light field, wherein the hard aperture comprises an iris diaphragm with a variable diameter and the method comprises the step of controlling the diameter of the collimated excitation light field by changing the size of the iris diaphragm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Further details and advantages of the invention are described in the following with reference to the attached drawings, which schematically show in:

[0052] FIGS. 1 to 3: Koehler integrator devices according to embodiments of the present invention;

[0053] FIGS. 4 to 5: multi-focal confocal microscopes according to embodiments of the present invention; and

[0054] FIG. 6: a conventional Koehler integrator (prior art).

PREFERRED EMBODIMENTS OF THE INVENTION

[0055] Features of preferred embodiments of the invention are described in the following with reference to the configuration of the Koehler integrator device and the integration thereof in a multi-focal confocal microscope. It is emphasized that the implementation of the invention is not restricted to the details of the optical design, but rather possible with changed parameters, in particular with changed numbers and pitch of the micro-lenses, changed focal lengths of the optical components and/or changed overall diameter of the optical components. Furthermore, the implementation of the invention is not restricted to the use of the Koehler integrator device in a multi-focal confocal microscope, but correspondingly possible in a lithography apparatus or with other illumination tasks with fixed or dynamically changing multiple spots. Details of operating a multi-focal confocal microscope, in particular features of the scanned structured sample excitation, are not described as they are known per se from conventional multi-focal confocal microscopes.

[0056] Embodiments of the Koehler Integrator Device and the Multi-Focal Confocal Microscope

[0057] FIG. 1 shows a first embodiment of the inventive Koehler integrator device 10, including the collimating lens 11, the first and second micro-lens arrays 12, 13, the collecting Fourier lens 14, the third micro-lens array 15 and the optional pinhole array 17, being arranged along the optical axis OA. Additionally, the Koehler integrator device 10 includes a casing and mechanical components holding the optical components in place (not shown). The mechanical components, like lens frames or micro-lens array frames, can be adapted for adjusting the position of the optical components along the optical axis and/or for exchanging optical components. The Koehler integrator device 10 is configured for creating an array of illumination spots in an image plane 2, where the optionally provided pinhole array 17 is located.

[0058] Light from a light source 111 is collimated with the collimating lens 11 having a focal length F.sub.CL (e. g. 60 mm). The collimated light field is relayed to the first micro-lens array 12, having a distance L.sub.1 (e. g. 50 mm) from the collimating lens 11. The first micro-lens array 12 comprises e. g. 33*33 micro-lenses 12A with a pitch p of e. g. 300 μm and a focal length ƒ (e. g. 5 mm). The second microlens array 13 has the identical properties like the first micro-lens array 12. Both micro-lens arrays 12, 13 have a mutual distance equal to the focal length f.

[0059] The Fourier lens 14 has a Fourier lens diameter (e. g. 500 mm) and a Fourier lens focal length F.sub.FL(e. g. 300 mm) defining a Fourier lens back focal plane 3 and a Fourier lens front focal plane 4. The second micro-lens array 13 is arranged in the Fourier lens back focal plane 3 and the third microlens array 15 is arranged in the Fourier lens front focal plane 4. The Fourier lens 14 superimposes light from all micro-lenses 13A of the second micro-lens array 13 in the third micro-lens array 15, which creates the array of illumination spots in the image plane 2.

[0060] The third micro-lens array 15 comprises a plurality of micro-lenses 15A having a common focal length ƒ.sub.x (e. g. 2 mm). The pitch p.sub.x of the micro-lenses 15A is selected in dependency on the magnification to be obtained with the multi-focal confocal microscope and the scanning range, and the number of the micro-lenses 15A is selected in dependency on the pitch and the field of view size to be obtained. With the practical application in a multi-focal confocal microscope, the third micro-lens array 15 comprises e. g. 100*100 micro-lenses with a 222 μm pitch.

[0061] To preserve the pitch and uniform spacing of the excitation spots, telecentric illumination of the third micro-lens array is provided by placing the Fourier lens 14, so that it's back focal plane overlaps with the second micro-lens array 13, and preferably by using the third micro-lens array 15 with a diameter smaller than the diameter of the Fourier lens 14. This will ensure that the pitch of the array of excitation spots remains constant and corresponds to the pitch p.sub.x of the third microlens array 15. Furthermore, this way, the pitch of the multi-focal excitation will be independent of the wavelength of light, unlike the array spots generated by a conventional Koehler integrator [9]. Without telecentric illumination, the pitch of the array of excitation spots would not correspond to the pitch of the micro-lenses 15A, and they would will vary spatially. This would become a problem when scanning the array of excitation spots across the sample, and would produce an uneven illumination of the reconstructed image. In particular, the image plane 2 containing the array of excitation spots may be conjugate to another image plane of the multi-focal confocal microscope containing an array of pinholes to filter the emission light. In this case, a varying pitch would not be matched with the filtering array of pinholes, and as a result the emission will be occluded and decrease in intensity away from the center of the optical path.

[0062] The pinhole array 17 is arranged in the front focal plane of the third micro-lens array 15, i. e. with a distance equal to the focal length ƒ.sub.x from the third micro-lens array 15. The pinhole array 17 comprises an opaque sheet, made of e. g. chrome on quartz with a thickness of e. g. 2 mm. A plurality of pinholes 17A are included in the sheet material, which are arranged like the micro-lenses 15A. Each of the pinholes 17A is aligned with the optical axis of one of the micro-lenses 15A. All pinholes 17 have the same diameter of e. g. 30 μm. In most applications of the Koehler integrator device 10, the front focal plane of the third micro-lens array 15, optionally with the pinhole array 17, represents the input plane of an apparatus including the Koehler integrator device 10, like the conjugate image plane of a multi-focal confocal microscope (see FIGS. 4 and 5).

[0063] The size of the excitation spots depends on the properties of the extended source as shown by a ray transfer matrix analysis (further details see below “Ray transfer matrix analysis”):

[00004]$\left(\begin{array}{c}{r}_{n,m}\\ {\theta }_{n,m}\end{array}\right)=\left(\begin{array}{c}\frac{f.Math.f_x}{F_{FL}{F}_{CL}}{R}_{source}+\frac{f_x}{F_{FL}}np\\ \left(\frac{f}{F_{FL}.Math.F_{CL}}+\frac{F_{FL}}{f.Math.f_x}\left(1-\frac{L}{F_{CL}}\right)\right)R_{source}+\\ \frac{F_{CL}.Math.F_{FL}}{f.Math.f_x}{\theta }_{source}+\left(\frac{1}{F_{FL}}-\frac{F_{FL}}{f.Math.f_x}\right)np+\frac{m{p}_x}{f_x}\end{array}\right)$

wherein r is the size of the excitation spots, θ the angular distribution, n is the index of the first and second micro-lens arrays 12, 13 and m the index of the third micro-lens array 15 (assuming n=0 and m=0 correspond to the micro-lenses centred on the optical axis). From this, np=R defines the radius of the beam incident on the first micro-lens array 12. The radius of the excitation spots can be rewritten as the first term, taken for maximal values of the extended source radius and the size of the beam incident on the first micro-lens array 12:

[00005]$r=\frac{f.Math.f_x}{F_{FL}.Math.F_{CL}}{R}_{source}+\frac{f_x}{F_{FL}}R$

[0064] There are two contributions determining the size the excitation spots: the size of the extended source R.sub.source and the radius R of the beam incident on the first micro-lens array 12. However, since ƒ and ƒ.sub.x are preferably on the order of a few millimetres, and F.sub.FL and F.sub.CL on the order of 10s to 100s of millimetres, the first term becomes negligible, while the second term will have a dominant effect on the size of the excitations spots.

[0065] FIG. 2 shows the provision of a light source device 110 with the Koehler integrator device 10 of FIG. 1. This light source device 110 can be provided e. g. in a multi-focal confocal microscope (see FIGS. 4, 5). The light source device 110 comprises a coherent light source 111, like a laser (e. g. type 488 nm wavelength continuous wave (CW) with M{circumflex over ( )}2<1.1, centre wavelength depending on the sample to be imaged), a focusing lens 112 and a rotating diffuser as a light scrambling device 113. The focusing lens 112 focusses the laser light field 111A through the light scrambling device 113 into the focal plane 5 of the collimating lens 11.

[0066] An alternative embodiment of the inventive Koehler integrator device 10 is shown in FIG. 3, wherein a beam sizing optic 16 is arranged between the collimating lens 11 and the first microlens array 12. Inserting the beam sizing optic 16 contracts the angular distribution of the extended light source 111. This in turn allows better focusing in the focal plane of the third micro-lens array 15. The inner rays 16A of the light field show the rays when the beam sizing optic 16 is in place, and the outer rays 16B show the rays without the beam de-expander 16. The beam sizing optic 16 comprises two lenses 16.1, 16.2 having focal lengths F.sub.1 (e. g. 120 mm) and F.sub.2 (e. g. 30 mm) with F.sub.2<F.sub.1 and being arranged with a distance F.sub.1+F.sub.2.

[0067] The beam sizing optic 16 shrinks the radius of the beam R to R*≅(F.sub.2/F.sub.1)R, without rejecting light. Introducing the beam sizing optic with the focal lengths F.sub.1 and F.sub.2 between the collimating lens 11 and the first micro-lens array 12, gives (further details see below “Ray transfer matrix analysis”):

[00006]$r=\frac{f.Math.f_x.Math.F_1}{F_{FL}.Math.F_{CL}.Math.F_2}{R}_{source}+\frac{f_x}{F_{FL}}$$R^{*}\cong \frac{f.Math.f_x.Math.F_1}{F_{FL}.Math.F_{CL}{F}_2}{R}_{source}+\frac{f_x.Math.F_2}{F_{FL}.Math.F_1}R$

[0068] As the beam sizing optic contracts the size of the beam (F.sub.2<F.sub.1), this results in a decrease in the diameter of the beam R by a factor of F.sub.2/F.sub.1. Although it also results in an inverse increase in the apparent size of the extended light source, since the second term carries a larger weight, the dominant effect is the decrease in the size of the excitation spots. With the provision of the beam de-expander 16, the pinhole array 17 to block excess light is therefore no longer required, improving the overall light transmission efficiency.

[0069] It should be noted that the quality of homogenization of the Koehler integrator device depends on the number of flat-fielding micro-lens channels over which the flat-field is averaged. Therefore, maximizing the number of micro-lens channels is usually preferred. Decreasing the radius of the beam incident on the first micro-lens array 12 with the beam sizing optic 16 may seem counterintuitive, as averaging over fewer micro-lens channels will reduce the homogeneity of the flat-field. Therefore, the beam sizing optic 16, in particular the focal lengths F.sub.1 and F.sub.2, preferably is configured for an optimization of the trade-off between homogeneity and spot size. For easier manipulation and optimization of this trade-off, it is preferred to use a variable beam de-expander to perform the light field contraction.

[0070] An alternative way to reduce the radius of the beam R is to put an iris (not shown) between the collimating lens and first micro-lens array 12. The iris would act as a mask and block light from passing through above a certain radius from the optical axis, effectively reducing the size of the beam incident on the first micro-lens array 12. This embodiment is preferred if power loss introduced by the iris is acceptable with the particular application of the inventive Koehler integrator device 10.

[0071] FIGS. 4 and 5 show exemplary embodiments of a multi-focal confocal microscope 100 including the inventive Koehler integrator device 120. Furthermore, the multi-focal confocal microscope 100 includes a light source device 110, a scanning device 130, a focusing optic 140 and a detector device 150 with a conjugate pinhole array 151 and an array detector camera 152. With the illustrated examples, light source device 110 comprises an incoherent light source 111, e. g. an LED, being focused with the focusing lens 112 into the Koehler integrator device 120. With the focusing optic 140, the array of excitation spots created with the Koehler integrator device 120 is imaged into the sample 1.

[0072] The scanning device 130 of FIG. 4 is any generic scanner, like e. g. galvanometer scanning mirror, creating a scanning pattern of excitation spots based on the spots array output by the Koehler integrator device 120. The scanning pattern is provided as known in multi-focal confocal microscopy. Alternatively, the scanning device 130 is provided by spinning discs 131, 132 upon which are mounted the third micro-lens array 15 and the pinhole array 151, resp., as shown in FIG. 5. The spinning discs 131, 132 have openings, which create the scanning pattern by disc rotation.

[0073] The inventive Koehler integrator device 10, e. g. as shown in FIGS. 1 to 3, is configured on the basis of the following design equations for its implementation in multi-focal confocal microscopes, e. g. according to FIGS. 4 and 5 (see also [8], [9]):

[0074] Fresnel Number:

[00007]$FN=\frac{p^2}{4\lambda f}$

[0075] For good homogeneity FN≳5

[0076] Flat field size:

[00008]$S=\frac{F_{FL}p}{f}$

[0077] Depends on size of the field of view and magnification [0078] Flat field size (at sample):

[00009]$S_{\mathrm{sample}}=\frac{1}{M}\frac{F_{FL}p}{f}$

[0079] Size of excitation spots (in focal plane of third micro-lens array 15):

[00010]$r=\frac{f.Math.f_x.Math.F_1}{F_{\mathrm{FL}}.Math.F_{\mathrm{CL}}.Math.F_2}{R}_{source}+\frac{f_x.Math.F_2}{F_{\mathrm{FL}}.Math.F_1}R$

[0080] (Depends on Magnification)

[0081] Size of excitation spots (at sample) should be diffraction limited:

[00011]$r_{\mathrm{sample}}=\frac{1}{M}\left(\frac{f.Math.f_x.Math.F_1}{F_{\mathrm{FL}}.Math.F_{\mathrm{CL}}.Math.F_2}{R}_{source}+\frac{f_x.Math.F_2}{F_{\mathrm{FL}}.Math.F_1}R\right)$

[0082] Flat Field Homogeneity:

[00012]$B=\frac{R}{p}$

[0083] For good homogeneity, B≳4

[0084] No-Crosstalk Condition:

[00013]$\frac{F_1.Math.f}{F_2.Math.F_{CL}}.Math.R_{source}\le \frac{p}{2}$

[0085] The design equations are functions of the following design parameters ƒ—focal length of flat-fielding micro-lens arrays 12, 13, p—pitch of micro-lens arrays 12, 13, ƒ.sub.x—focal length of third micro-lens array 15, p.sub.x—third micro-lens array 15, F.sub.FL—focal length of Fourier lens 14, F.sub.CL— focal length of collimating lens 11, F.sub.1— focal length of first beam expander lens 16.1, F.sub.2— focal length of second beam expander lens 16.2, R.sub.source—radius of extended light source 111, R.sub.source—angular divergence of extended light source 111, M—magnification, R—beam radius incident on the first micro-lens array 12 without the beam expander 16 (can be estimated as: R≅R.sub.source+F.sub.CL tan(θ.sub.source) (further details see below “Ray transfer matrix analysis”), and λ—wavelength.

[0086] Furthermore, in the case of laser illumination, the size and the divergence of the extended light source 111 can be controlled by displacing the rotating diffuser, changing the focal length of the focusing lens and its position, respectively. Changing the position of the focusing lens also affects the size of the beam hitting the rotating diffuser, so this can also be used to change the size of the extended light source.

[0087] The above design equations can be used for designing the components for implementing the inventive Koehler integrator device 120 to multi-focal confocal systems.

[0088] Ray Transfer Matrix Analysis

[0089] For designing the inventive Koehler integrator device, it is advantageous to perform a ray transfer matrix calculation for the whole Koehler integrator device. In particular, the ray transfer matrix analysis can be used for determining how the size of the excitation spots depends on the properties of the extended light source.

[0090] To fully explore the effect of introducing the beam sizing optic (see FIG. 3) between the collimating lens and the first micro-lens array, the two cases are compared side-by-side. For this, the system is divide into three parts (y.sub.1, β.sub.1).fwdarw.(y.sub.2, β.sub.2), (x.sub.1, α.sub.1).fwdarw.(x.sub.2, α.sub.2), and (z.sub.1, γ.sub.1).fwdarw.(z.sub.2, γ.sub.2) (see FIGS. 1, 3):

[0091] (1) The sub-system 1 (y.sub.1, β.sub.1).fwdarw.(y.sub.2, R.sub.2) starts at the light source 111 and ends in a plane containing the first micro-lens array 12, but without considering its effect. y.sub.2 effectively determines the radius of the beam incident on the first micro-lens array 12 (R).

[0092] Without the Beam Sizing Optic:

[00014]$\left(\begin{array}{c}{y}_2\\ {\beta }_2\end{array}\right)=\left(\begin{array}{c}\left(1-\frac{L}{F_{\mathrm{CL}}}\right)y_1+F_{\mathrm{CL}}{\beta }_1\\ -\frac{y_1}{F_{\mathrm{CL}}}\end{array}\right)$

[0093] Where L is the variable distance between the collimating lens and the first micro-lens array. With the beam sizing optic 16:

[00015]$\left(\begin{array}{c}{y}_2\\ {\beta }_2\end{array}\right)=\left(\begin{array}{c}\frac{1}{F_{\mathrm{CL}}.Math.F_1.Math.f_2}\left(F_2^2\left(L_1-F_{\mathrm{CL}}-F_1\right)+F_1^2\left(L_2-F_2\right)\right)y_1-\frac{F_2}{F_1}{F}_{\mathrm{CL}}{\beta }_1\\ \frac{F_1}{F_{\mathrm{CL}}}\frac{y_1}{F_{\mathrm{CL}}}\end{array}\right)$

[0094] Where L.sub.1 and L.sub.2 are the distances between the collimating lens 11 and the first lens 16.1 of the beam sizing optic 16, and the distance between the second lens 16.2 of the beam sizing optic 16 and the first micro-lens array 12.

[0095] (2) The sub-system 2 (x.sub.1, α.sub.1).fwdarw.(x.sub.2, α.sub.2) starts in local coordinate system of a single micro-lens 12A of the first micro-lens array 12 and ends in the focal plane of the Fourier lens 14, containing the third micro-lens array, but without considering its effect

[00016]$\left(\begin{array}{c}{x}_2\\ {\alpha }_2\end{array}\right)=\left(\begin{array}{c}-\frac{F_{\mathrm{FL}}}{f}{x}_1\\ -\frac{1}{F_{\mathrm{FL}}}\left({\alpha }_{1}f-np\right)\end{array}\right)$

(Not explicitly modified by introduction of beam sizing optic.)

[0096] (3) The sub-system 3: (z.sub.1, γ.sub.1).fwdarw.(z.sub.2, γ.sub.2) starts in local coordinate system of a single micro-lens 15A of the third micro-lens array 15 and ends in local focal plane of a single micro-lens 15A of the third micro-lens array 15

[00017]$\left(\begin{array}{c}{z}_2\\ {\gamma }_2\end{array}\right)=\left(\begin{array}{c}{f}_x{\gamma }_1\\ {\gamma }_1-\frac{z_1}{f_x}\end{array}\right)$

(Not explicitly modified by introduction of beam expander.)

[0097] These three subsystems are linked together by boundary conditions that transition from the local coordinate systems of micro-lens arrays 12, 15 to the global coordinate system. The boundary conditions are:

[0098] Boundary condition (y.sub.2, β.sub.2).fwdarw.(x.sub.1, α.sub.1): from global coordinate system to the local coordinate system of the flat-fielding micro-lens arrays

[00018]$\left(\begin{array}{c}{x}_1\\ {\alpha }_1\end{array}\right)=\left(\begin{array}{c}{y}_2-np\\ {\beta }_2\end{array}\right)$

[0099] Boundary condition (x.sub.2, α.sub.2).fwdarw.(z.sub.1, γ.sub.1): from global coordinate system to the local coordinate system of the excitation micro-lens array

[00019]$\left(\begin{array}{c}{z}_1\\ {\gamma }_1\end{array}\right)=\left(\begin{array}{c}{x}_2-m{p}_x\\ {\alpha }_2\end{array}\right)$

[0100] Regardless of the elements before the first micro-lens array 12, the ray-tracing matrix between the first micro-lens array 12 and the focal plane of the third micro-lens array is given by (adapted from [6]):

[00020]$\left(\begin{array}{c}{z}_2\\ {\gamma }_2\end{array}\right)=\left(\begin{array}{c}-\frac{f_x}{F_{FL}}\left({\beta }_{2}f-np\right)\\ \frac{F_{FL}}{f_x.Math.f}{y}_2-\frac{f}{F_{FL}}{\beta }_2\left(\frac{1}{F_{FL}}-\frac{F_{FL}}{f.Math.f_x}\right)np+\frac{m{p}_x}{f_x}\end{array}\right)\cong \left(\begin{array}{c}-\frac{f_x}{F_{FL}}\left({\beta }_{2}f-y_2\right)\\ -\frac{f}{F_{FL}}{\beta }_2+\frac{1}{F_{FL}}{y}_2+\frac{m{p}_x}{f_x}\end{array}\right)$

[0101] Where np indicates the radius of the beam incident on the first micro-lens array 12, equally corresponding to the maximal height of a beam incident on the array 12, R=max(y.sub.2). Similarly, the maximal values of y.sub.1, β.sub.1 are set by the radius and angular divergence of the extended light source 111:

max(y.sub.1)=R.sub.source

max(β.sub.1)=θ.sub.source

[0102] By replacing the values of y.sub.2 and β.sub.2 into the system with or without a beam sizing optic, it can be shown that the overall size of the excitation spots can be minimized more effectively in the case including the beam sizing optic 16. To find the size of the excitation spot r, compute the maximum of z.sub.2, r=max(z.sub.2) is computed:

Without Beam Expander

[0103] [00021]$r\cong \frac{f_x}{F_{FL}}\left(1-\frac{L}{F_{CL}}+\frac{f}{F_{CL}}\right)R_{\mathrm{source}}+\frac{f.Math.F_{CL}}{F_{FL}}{\theta }_{source}$

[0104] Where L is the distance between the collimating lens and the first flat-fielding micro-lens array.

[0105] A few interesting solutions can be identified, which facilitate the contraction of the beam sizing optic, but are not obligatory:

[0106] If L=F.sub.CL, the beam height: y.sub.2=F.sub.CLβ.sub.1 is set purely by divergence of extended source, the beam radius: R=F.sub.CLθ.sub.source is set purely by divergence of extended light source, and the spot size is about

[00022]$r\cong \frac{f_x.Math.f}{F_{\mathrm{FL}}.Math.F_{\mathrm{CL}}}{R}_{\mathrm{source}}+\frac{f.Math.F_{\mathrm{CL}}}{F_{\mathrm{FL}}}{\theta }_{\mathrm{source}}$

[0107] If L=F.sub.CL−ƒ, the beam height is

[00023]$y_2=\frac{f}{F_{CL}}{y}_1+F_{CL}{\beta }_1,$

the beam radius is

[00024]$R=\frac{f}{F_{CL}}{R}_{source}+F_{CL}{\theta }_{sou\mathrm{rce}},$

and the spot size

[00025]$r\cong \frac{f.Math.F_{CL}}{F_{FL}}{\theta }_{source}$

is set purely by divergence of extended source.

[0108] With beam sizing optic

[00026]$r\cong \frac{f_x}{F_{FL}.Math.F_{CL}}\left(\frac{F_2}{F_1}\left(L_1-F_{CL}-F_1\right)+\frac{F_1}{F_2}\left(L_2-F_2\right)-\frac{f.Math.F_1}{F_2}\right)R_{source}+\frac{f.Math.F_{CL}.Math.F_2}{F_{FL}.Math.F_1}{\theta }_{source}$

[0109] Where L.sub.1 is the distance between the collimating lens 11 and the first beam expander lens 16.1, and L.sub.2 the distance between the second beam expander lens 16.2 and the first micro-lens array 12. Since the second term of the expression for r dominates, it can be seen that introducing a beam sizing optic rescales the size of the excitation foci by a factor of F_2/F_1. In the case where F_2<F_1, this leads to a decrease in size. Optional modification of L.sub.1 and L.sub.2 allows a flexible tuning of the radius R.

[0110] A couple of interesting solutions can be identified which facilitate the contraction by the beam sizing optic 16, but are not obligatory:

[0111] If L.sub.1=F.sub.1+F.sub.CL and L.sub.2=F.sub.2, the beam height

[00027]$y_2=-\frac{F_2}{F_1}{F}_{CL}{\theta }_1$

is set purely by divergence of extended source, the beam radius:

[00028]$R^{*}=-\frac{F_2}{F_1}{F}_{CL}{\theta }_{source}$

is set purely by divergence of extended source, and the spot size is

[00029]$r=\frac{f_x.Math.F_1.Math.f}{F_{\mathrm{FL}}.Math.F_{\mathrm{CL}}.Math.F_2}{R}_{source}+\frac{f.Math.F_{\mathrm{CL}}.Math.F_2}{F_{FL}.Math.F_1}{\theta }_{source}.$

[0112] If L.sub.1=F.sub.1 and L.sub.2=F.sub.2, the beam height is

[00030]$y_2=-\frac{F_2}{F_1}\left(y_1+F_{CL}{\beta }_1\right),$

the beam radius is

[00031]$R^{*}=-\frac{F_2}{F_1}\left(R_{source}+F_{CL}{\theta }_{source}\right),$

and the spot size is

[00032]$r=\frac{f_x}{F_{FL}.Math.F_{CL}}\left(-\frac{F_2}{F_1}{F}_{CL}+\frac{f.Math.F_1}{F_2}\right)R_{source}+\frac{f.Math.F_{\mathrm{CL}}.Math.F_2}{F_{FL}.Math.F_1}{\theta }_{source}.$

[0113] If

[00033]$L_2=\frac{F_2}{F_1}\left(F_1+F_2\right),$

the beam height

[00034]$y_2=-\frac{F_2}{F_1}\left(1-\frac{L_1}{F_{CL}}\right)y_1-\frac{F_2}{F_1}{F}_{CL}{\beta }_1$

provides direct rescaling between cases with and without a beam expander, beam radius

[00035]$R^{*}=-\frac{F_2}{F_1}\left(1-\frac{L_1}{F_{CL}}\right)R_{source}-\frac{F_2}{F_1}{F}_{CL}{\theta }_{source}$

provides direct rescaling between cases with and without a beam expander, and spot size is

[00036]$r=\frac{f_x.Math.F_2}{F_{CL}.Math.F_{FL}.Math.F_1}\left(1-\frac{L_1}{F_{CL}}\right)R_{source}+\frac{f.Math.F_{\mathrm{CL}}.Math.F_2}{F_{FL}.Math.F_1}{\theta }_{source}$

[0114] The features of the invention disclosed in the above description, the drawings and the claims can be of significance individually, in combination or sub-combination for the implementation of the invention in its different embodiments.