METHOD AND SYSTEM FOR CHARACTERIZING A FOCUSING OPTICAL ELEMENT

Abstract

A method for characterizing a focusing optical element comprises transmitting a light beam through the optical element such that the light beam is focused at a focal plane, collecting the light beam by a collection assembly, and detecting the light beam by an image detector. The method further comprises providing a scattering element between the optical element and the collection assembly such that the light beam generates a scattered reference wave, collecting the light beam and the reference wave, and detecting the light beam and the reference wave by the detector. The light beam and the reference wave partly overlap at the detector. Moreover, the method comprises determining an influence of the optical element on a wave front of the light beam based on the light beam and the reference wave. A system and a use of a system for characterizing a focusing optical element are further disclosed.

Claims

1. A method for characterizing a focusing optical element, the method comprising: transmitting a light beam through the focusing optical element such that the light beam is focused at a focal plane by the focusing optical element; collecting the focused light beam after the focal plane by a beam collection assembly and detecting the collected light beam by an image detector; providing a scattering element comprising or consisting of a nanoparticle between the focusing optical element and the beam collection assembly such that the light beam generates a scattered reference wave; collecting the focused light beam and at least a part of the scattered reference wave after the focal plane by the beam collection assembly and detecting the collected light beam and the collected reference wave by the image detector, wherein the detected light beam and the detected scattered reference wave partly overlap with each other at the image detector; and determining an influence of the focusing optical element on a wave front of the transmitted light beam based on the detected light beam and the detected scattered reference wave.

2. The method according to claim 1, wherein the scattering element is consecutively placed at different transversal positions of the light beam and wherein the collected light beam and at least the part of the scattered reference wave are detected for each transversal position of the scattering element.

3. The method according to claim 1, wherein the scattering element is arranged in the focal plane or within a longitudinal distance of ±2 mm from the focal plane.

4. The method according to claim 1, wherein the scattering element is adapted such that the reference wave generated by the light beam essentially comprises predetermined orders of electric and/or magnetic multipole radiation.

5. The method according to claim 4, wherein the scattering element is adapted such that the reference wave generated by the light beam essentially corresponds to electric dipole radiation and optionally electric quadrupole radiation.

6. The method according to claim 1, wherein the nanoparticle has a far-field emission of scattered light comprising or consisting of a predetermined and known dipole mode and/or predetermined and known quadrupole mode.

7. The method according to claim 1, wherein several different scattering elements are used in consecutive measurements for generating the reference wave.

8. The method according to claim 1, wherein collecting the focused light beam and optionally at least the part of the scattered reference wave comprises collimating the light beam and optionally imaging the light beam to the image detector.

9. The method according to claim 1, wherein the light beam is provided with a predetermined polarization.

10. The method according to claim 1, wherein the light beam is provided in consecutive measurements with different predetermined polarizations.

11. The method according to claim 1, wherein collecting and detecting the focused light beam and at least the part of the scattered reference wave is carried out such that a first region of an image detected by the image detector corresponds to an overlap of the light beam and the reference wave and a second region of the image detected by the image detector essentially corresponds only to the part of the reference wave.

12. The method according to claim 11, wherein determining the influence of the focusing optical element on the wave front of the transmitted light beam includes determining an intensity distribution of the first part of the image detected by the image detector and determining an intensity distribution of the second part of the image detected by the image detector.

13. The method according to claim 12, further including fitting a calculated far-field emission of multipole radiation to an intensity distribution of the second region of the image detected by the image detector for characterizing the reference wave.

14. A system for characterizing a focusing optical element, the system comprising: a beam collection assembly for collecting a light beam transmitted through and focused at a focal plane by the focusing optical element to be characterized, wherein the beam collection assembly is adapted to collect the focused light beam after the focal plane; a scattering element comprising or consisting of a nanoparticle, wherein the scattering element is arrangeable in the light beam between the focusing optical element and the beam collection assembly such that the light beam generates a scattered reference wave and wherein the scattering element is removable from the light beam; an image detector for detecting the collected light beam and at least a part of the generated scattered reference wave, wherein the detected scattered reference wave and the light beam partly overlap with each other at the image detector; and a computing unit which is adapted to determine an influence of the focusing optical element on a wave front of the transmitted light beam based on the detected light beam and the detected partly overlapping scattered reference wave.

15. The system according to claim 14, wherein the beam collection assembly comprises a collimating optical element and optionally one or more imaging optical elements.

16. The system according to claim 15, wherein the collimating optical element is a microscope objective lens and optionally an immersion type microscope objective lens.

17. The system according to claim 15, wherein the collimating optical element is chosen to have a larger numerical aperture than the focusing optical element to be characterized.

18. The system according to claim 14, wherein the image detector corresponds to a camera.

19. The system according to claim 14, wherein the nanoparticle has a far-field emission of scattered light comprising or consisting of a predetermined and known dipole mode and/or a predetermined and known quadrupole mode.

20. A process of utilizing the system according to claim 14, the process comprising: determining optical aberrations of a wave front of a light beam caused by a focusing optical element to be characterized when transmitting a light beam through the focusing element.

21. The process according to claim 14, wherein the focusing optical element to be characterized is a microscope objective lens.

22. A method for characterizing a scattering element, the method comprising: transmitting a light beam through a focusing optical element such that the light beam is focused at a focal plane by the focusing optical element; collecting the focused light beam after the focal plane by a beam collection assembly and detecting the collected light beam by an image detector; providing the scattering element comprising or consisting of a nanoparticle to be characterized between the focusing optical element and the beam collection assembly such that the light beam generates a scattered sample wave; collecting the focused light beam and at least a part of the scattered sample wave after the focal plane by the beam collection assembly and detecting the collected light beam and the collected sample wave by the image detector; and determining an influence of the scattering element arranged in the light beam on a wave front of the transmitted light beam based on the detected light beam and the detected scattered sample wave.

23. The method according to claim 22, wherein the scattering element is consecutively arranged at different transversal positions of the light beam and wherein the collected light beam and at least the part of the scattered sample wave is detected for each transversal position of the scattering element.

24. The method according to claim 22, wherein the scattering element is arranged in the focal plane or within a longitudinal distance of ±2 mm from the focal plane.

25. The method according to claim 22, wherein the nanoparticle has a far-field emission of scattered light comprising or consisting of a predetermined and known dipole mode and/or a predetermined and known quadrupole mode.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Further optional examples will be illustrated in the following with reference to the drawings.

[0039] FIG. 1 depicts a system for characterizing a focusing optical element according to an optional example of the disclosure.

[0040] FIGS. 2A and 2B show intensity profiles taken according to a method according to an optional example.

[0041] FIG. 3 depicts images taken according to a method according to an optional example together with the reconstruction of the phase distribution of the light beam.

[0042] In the drawings the same reference labels are used for corresponding or similar features in different drawings.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0043] FIG. 1 depicts a system 10 according to an optional example for characterizing a focusing optical element 12. The focusing optical element 12 interacts with the system 10 but does not form part of the system 10.

[0044] The system 10 serves the purpose of characterizing the focusing optical element 12 with respect to possible aberrations imposed on the light beam 100 transmitted through the focusing optical element 12. According to the present example the focusing optical element 12 is a microscope objective lens. The focusing optical element 12 under test focuses a light beam 100 coupled into the focusing optical element 12 into a focal plane 1000.

[0045] The system 10 comprises a beam collection assembly 14 for collecting and collimating the divergent and previously focused light beam 100 and transmitting the light beam 100 to an image detector 16 forming part of the system 10. According to the presented example the beam collection assembly 14 comprises several further optical elements, wherein one of these optical elements is a collimating element 18 for fully or partly collimating the divergent light beam 100 after the focus in the focal plane 1000. The beam collection assembly 14 according to the presented example further comprises additional optional optical elements 20 for an optional polarization analysis of the light beam 100, such as liquid crystal variable retarders and a linear polarizer. The beam collection assembly 14 finally comprises an imaging lens 22 for imaging the back focal plane of the collecting optical element 18 to the image detector 16 to retrieve the angular distribution of the collected signal.

[0046] According to the presented example the image detector 16 is adapted as a digital camera having a two-dimensional array of sensor pixels for detecting a spatial intensity distribution.

[0047] Moreover, the system 10 comprises a scattering element 24 arranged between the focusing optical element 12 and the beam collection assembly 14 in the focal plane 1000 or close to it. According to the preferred example the scattering element 24 comprises a nanoparticle, which generates a scattered reference wave 26 when irradiated with the focused light beam 100. As indicated in FIG. 1, the scattering element 24 may be supported by a transparent slide, such as a glass slide, which allows arranging the scattering element 24 at the desired position in the focal plane 1000 and optionally directly in the focus or adjacent to it to generate a scattered reference wave 26. The reference label 24 indicates the supporting transparent slide, since individual nanoparticles forming the actual scattering elements 24 are too small to be presented in this schematic sketch. The space between the glass slide and the collecting optical element may be filled with an immersion oil 25.

[0048] Scattered reference wave is indicated in the figure by the area marked with a reference label 26. This scattered reference wave 26 extends from the scattering element 24 arranged in or close to the focus of focal plane of the light beam 100 and is at least partly collected and collimated by the collimating optical element 18 of the beam collection assembly 14. Accordingly, when the scattering element 24 is arranged in the light beam 100, in particular in the focus of the light beam 100, this scattered reference wave 26 is generated and transmitted through the beam collection assembly 14 together with the collected and collimated light beam 100. It is to be noted that this scattered reference wave 26 is generated only in the focus after the focusing optical element 12 under test and therefore is not subject to possible optical aberrations of the focusing optical element 12 under test.

[0049] According to the presented example the collimating optical element 18 has a higher numerical aperture than the focusing optical element 12 under test. This allows for collecting and collimating parts of the scattered reference wave 26 having a larger divergence than the divergent light beam 100 after the focus. The beam collection assembly 14 and the image detector 16 are adapted to image the transmitted light beam 100 and the overlapping scattered reference wave 26 to a first region of the image detected by the image detector 16 and in addition image and additional part of the scattered reference wave 26 to a second region of the image detector 16 not overlapping with the light beam 100. Said part of the scattered reference wave 26 imaged to the second region of the detected image may be that part of the scattered reference wave 26 collected and collimated by the outer area of the collimating optical element 18 exceeding the numerical aperture of the focusing optical element 12 under test. Accordingly, the larger the difference between the numerical apertures of the collimating optical element 18 in the focusing optical element 14, the larger the second region of the detected image corresponding solely to the reference wave 26 is.

[0050] For characterizing the focusing optical element 12, images may be detected with and without the scattered reference wave 26 overlapping the detected light beam 100 on the detector 16. This may be achieved in consecutive measurements, wherein the measurement with the scattered reference wave 26 overlapping the light beam 100 may be carried out with the system 10 as described above, and therein the measurement of the light beam 100 without the scattered reference wave 26 overlapping may be carried out in a separate measurement with the scattering element 24 being removed from the focus and the light beam 100. This may be achieved for instance by moving the transparent slide carrying the scattering element 24 at least partly parallel to the focal plane to move the scattering element 24 out of the focus, as indicated by arrow 1002.

[0051] With reference to FIGS. 2A and 2B a method for characterizing a focusing optical element 12 according to an optional example is described. The method according to the presented example uses a system 10, as presented with reference to FIG. 1. The method uses a nanoparticle as a scattering element 24, which is placed in the focal plane of the focusing optical element 12 and the collimating optical element 18, which both share the same focal plane 1000. The scattering element 24 can be removed from the focus and/or the light beam 100 to carry out measurements without the scattering element 24 arranged in the focus and the light beam 100.

[0052] The method further comprises optional polarization measurements which are performed by controlling liquid crystals, which form part of the additional optical elements 20 of beam collection assembly 14. For example, various measurements may be carried out for linear polarization having polarization angles of 0°, 45°, 90° and 135°, as well as for left-and right-handed circular polarization.

[0053] For each of the polarizations an image is detected of the light beam 100 and the scattered reference wave 26 collected and collimated by the beam collection assembly 14 and imaged to the image detector 16. Afterwards the scattering element 24 is removed from the focus and the light beam 100 and the measurements are repeated. The order of carrying out the measurements may be changed or reversed.

[0054] The measurements and the changes of the system 10 between the individual measurements are carried out in an automated manner, i.e., the change of the polarization controlling optical elements and/or the removal or inserting of the scattering element into the focus are carried out in an automated manner.

[0055] FIG. 2A schematically illustrates the image detected by the image detector 16 for measurements when the scattering element 24 is placed in the focus of the light beam 100 and generates the scattered reference wave 26. The focusing optical element 12 under test is a microscope objective lens of the type LEICA HCX PL FLUOTAR 100x/0.9. The used collimating optical element 18 is a microscope objective lens of the type LEICA HCX FLUOTAR 100x/1.32 OIL. Accordingly, the detected image represents an intensity distribution of the light beam 100 and the scattered reference wave 26 at a detection plane of the image detector 16, which corresponds to an angular distribution of the light beam 100 and the reference wave 26 after the focus. The light beam 100 is a Gaussian beam having a central wavelength of 680 nm, a spectral width Δλ≈5 nm and a beam waist w.sub.0=3 mm. The detected image comprises a first region 104 in the center of the detected image and a second region 106 surrounding the centered first region 104. The first region 104 corresponds to an intensity distribution, in which the light beam 100 and the scattered reference wave 26 are overlapping and interfering, which results in the intensity distribution of the first region 104. The second region 106 originates solely from the scattered reference wave 26, which has a larger divergence than the light beam 100 after the focus and therefore spreads around the central first region 104 in the detected image. As can be seen, the intensity of the light beam in the first region 104 exceeds the intensity of the scattered reference wave 26 in the second region by far.

[0056] However, the isolated image of the scattered reference wave 26 in the second region 106 allows fitting and/or reconstructing the whole profile of the scattered reference wave 26, as will be explained in detail further below.

[0057] The image in FIG. 2B shows the intensity distribution of the light beam 100 without an overlapping scattered reference wave 26. This image was taken with the scattering element 24 removed from the focus and the light beam 100 such that no scattered reference wave is generated. This allows detecting solely the light beam 100 with the image detector without an overlapping reference wave.

[0058] In the following, a retrieval of the phase front of the light beam 100 and the determination of the influence of the focusing optical element on a wave front of the transmitted light beam according to an optional example are described.

[0059] When measuring with the scattering element 24 in the focused light beam 100, the first region 104 of the intensity profile shows the interference between the transmitted light beam 100 and the scattered reference wave 26 generated by the scattering element 24. When the scattering element 24 is not placed in the focus and the light beam 100, the intensity profile of the light beam 100 is measured without the scattered reference wave 26 overlapping.

[0060] For retrieving the phase front of the scattered reference wave 26 in the central first region 104, the far-field emission of dipoles is calculated for an emitter, i.e., a scattering element 24, placed on a glass substrate. Theoretical far-fields are fitted to the outer second region 106 of the detected image where only the scattered reference wave 26 is recorded. According to the presented optional example, for these fits, the amplitudes and phases of the multipole contributions, which are in the present case limited to dipole contributions, serve as free parameters. A full set of Stokes parameters may be measured before and provided in order to prevent ambiguities during the identification of the generated dipole moments. The distance of the scattering element 24 above the surface is determined by a fit as well. The distance of the scattering element 24 from the surface of the glass slide may correspond to the radius or half thickness of the scattering element 24. Once the fit has converged, the retrieved parameters can be used to calculate the emission of the excited dipole moments to the whole three-dimensional space. In our case, we are especially interested in calculating the emission in the central first region 104 of the detected image. Knowing the dipole moments allows calculating the far-fields also in the central first region, i.e., in the region covered by the numerical aperture of the focusing optical element 12 under test, where interference with the transmitted light beam 100 is observed.

[0061] At this point we now have the following information in the inner region of the detected image:

[0062] I.sub.1, which indicates the intensity distribution of the transmitted light beam 100; I.sub.2, which indicates the intensity distribution of the scattered reference wave 26;

I.sub.tot, which indicates the resulting intensity distribution of the interference of components I.sub.1 and I.sub.2.

[0063] Furthermore, the phase distribution of the scattered reference wave φ.sub.2 is known, as the scattered light in the central first region 104 of the detected image was calculated from the fitted dipole moments and therefore contains full amplitude and phase information. Using the following standard equation for two interfering light fields

I.sub.tot=I.sub.1+I.sub.2+2√{square root over (I.sub.1I.sub.2)}.Math.cos(φ.sub.1−φ.sub.2)

we can see that the only unknown component in equation (1) is φ.sub.1, which indicates the phase distribution of the light beam 100, which therefore can be calculated easily.

[0064] In other words, the exact information including intensity I.sub.2 and phase φ.sub.2 distributions of the scattered reference wave is used for the characterization of the focusing optical element 12.

[0065] It is emphasized that the focusing optical element 12 under test is the only optical element, through which the light beam 100 is transmitted but the scattered reference wave 26 is not transmitted. The light beam 100 and the scattered reference wave 26 are transmitted through all optical elements of the system 10 in an equal manner. This bears the significant advantage that possible aberrations, which are possibly caused by the optical elements of the system 10 equally affect the light beam 100 and the scattered reference wave 26. Thus, the only aberrations affecting the light beam 100 but not the scattered reference wave 26 essentially originate in the focusing optical element 12 under test. Consequently, the system 10 and method allow an undistorted characterization of the focusing optical element 12 under test. Therefore, the system is invariant to phase distortions of all other subsequent components in the system.

[0066] As a further optional step, the lowest order Zernike polynomials (piston, tip, tilt, defocus) may be fitted and subtracted from the calculated distributions, as these contributions are of minor importance for the characterization of the focusing optical element 12 under test. These contributions can be influenced and/or corrected by tilting and/or moving the focusing optical element 12 and therefore usually are not considered as an aberration caused by the focusing optical element 12.

[0067] The method for characterizing the focusing optical element 12 may be partly or fully automated. For instance, the method may be carried out by a computer program. The computer program may, for instance, be configured to include one or more of the following functionalities: controlling a piezo table for controlling the position of the scattering element 24, controlling a light source, recording data provided by the image detector 16 and/or possible further sensors; controlling a voltage applied to optional liquid crystal cells for polarization analysis; triggering the image detector 16.

[0068] The evaluation of the detected image may also be automatedly carried out by a computer program. For example, the computer program may be written with a conventional mathematical programing environment, such as MATLAB.

[0069] FIG. 3 exemplarily indicates detected images for the characterization of a microscope objective lens as the focusing optical element 12 under test. For the measurement, a laser beam having a central wavelength of 680 nm was selected as light beam 100. The scattering element 24 is provided as a spherical silicon nanoparticle having a radius of 76 nm attached to a glass slide. The sections of FIG. 3 depict the detected image of the intensity profile with the scattering element 24 placed in the focus of the light beam 100 (section a) and with the scattering element 24 removed from the focus and the light beam 100 (section b). Section c) indicates calculated emission pattern for the retrieved dipole moments, i.e., the retrieved intensity distribution of the scattered reference wave by calculation Section d) depicts the reconstructed phase distribution of the k-spectrum of the light beam 100 as focused by the microscope objective lens, which is the focusing optical element 12 under investigation. For illustrative purposes, the lowest order Zernike polynomials (Piston, Tip, Tilt, Defocus) are fitted and subtracted. Section d) clearly shows a crescent-shaped deformation of the phase front indicating the presence of aberrations induced by the microscope objective lens. This explains the corresponding distortion of the total intensity I.sub.tot as illustrated in section a), although the individual intensity distributions I.sub.1 of the light beam 100 and I.sub.2 of the scattered reference wave 26 look rather symmetric (see sections b) and c)).

[0070] According to the presented example, a nanoparticle was chosen as the scattering element 24 emitting a scattered wave essentially corresponding to a dipole far-field emission. However, according to other examples different scattering elements 24 may be chosen, which may comprise an emission including other multipole orders. The preferred multipole modes of the emission of the scattering element may be considered when fitting the intensity and/or phase distribution of the scattered reference wave 26. Selecting a scattering element 24 having a known and predetermined emission comprising or consisting of predetermined multipole orders may facilitate the fitting process and reduce ambiguities. Keeping the multipole orders low, i.e., restricted to dipole and optionally to quadrupole orders, may have the benefit of reducing the required computational effort for the fitting process.

[0071] It should be noted that this method is not restricted to the chosen wavelength. Although for a fixed nanostructure the potential spectral range may be limited, by using particles of other sizes, the available range can span the whole visible and near-infrared spectrum. Furthermore, it is also not necessary to use a perfectly spherical nanoparticle, since this procedure is capable of identifying arbitrary combinations of dipoles. As long as the scattering element features a reasonably strong dipole response and simultaneously suppresses higher order multipoles, it is possible to use almost arbitrarily shaped nanostructures. As an example, metal cylinders (e.g., made from gold etc.) may be used as an alternative to the spherical nanoparticles. Using modern lithography, cylindrical nanostructures can be fabricated easily in arrays including different sizes, hence providing a full range of different probes on a single sample to cover and measure over a wide spectral range.

LIST OF REFERENCE LABELS

[0072] 10 system for characterizing a focusing optical element [0073] 12 focusing optical element [0074] 14 beam collection assembly [0075] 16 image detector [0076] 18 collimating optical element [0077] 20 (optional) additional optical elements [0078] 22 imaging lens [0079] 24 scattering element (attached to glass slide) [0080] 25 immersion oil [0081] 26 scattered reference wave [0082] 100 light beam [0083] 104 first region of image [0084] 106 second region of image [0085] 1000 focal plane [0086] 1002 sliding direction for removal of scattering element