METHOD AND APPARATUS FOR MEASURING A CURVED WAVEFRONT USING AT LEAST ONE WAVEFRONT SENSOR

Abstract

With regard to a particularly precise measurement of a wavefront using structurally simple means, a method for measuring a curved wavefront using a wavefront sensor is specified, wherein a plurality of measurements are carried out at different positions along the wavefront using at least one wavefront sensor in order to determine a local gradient of the wavefront at the different positions, which method is characterized in that the plurality of measurements are carried out in each case with a substantially tangential alignment of a light entrance plane of the wavefront sensor(s) with the curved wavefront. A corresponding apparatus for measuring a curved wavefront using a wavefront sensor is also specified.

Claims

1. A method for measuring a curved wavefront using at least one wavefront sensor, wherein a plurality of measurements are carried out at different positions along the wavefront using at least one wavefront sensor in order to determine a local gradient of the wavefront at the different positions, characterized in that the plurality of measurements are carried out in each case with a substantially tangential alignment of a light entrance plane of the wavefront sensor(s) with the curved wavefront.

2. The method according to claim 1, characterized in that the wavefront sensor is a Shack-Hartmann sensor.

3. The method according to claim 1 or 2, characterized in that the Shack-Hartmann sensor or wavefront sensor is aligned at the different positions in such a manner that a function f(.sub.1, .sub.2, . . . , .sub.N), which is dependent on at least one displacement .sub.k of a focal point from a reference point of a microlens of the Shack-Hartmann sensor or wavefront sensor, is minimized, wherein the displacement .sub.k of the associated focal point corresponds to an image of a local inclination in the wavefront by means of the respective microlens.

4. The method according to claim 3, characterized in that the function f(.sub.1, .sub.2, . . . , .sub.N) represents the weighted average of all the displacements .sub.k or the weighted average of the squares of all the displacements .sub.k.

5. The method according to claim 3 or 4, characterized in that the alignment of one or more wavefront sensors is carried out in such a manner that the displacement(s) .sub.k is/are as small as possible or below a predeterminable threshold value.

6. The method according to any one of claims 1 to 5, characterized in that the alignment of one or more wavefront sensors is carried out in each case before a measurement and/or between two or more measurements.

7. The method according to any one of claims 1 to 6, characterized in that the alignment of one or more wavefront sensors is carried out continuously during a movement of one or more wavefront sensors.

8. The method according to any one of claims 1 to 7, characterized in that the wavefront sensor(s) is/are moved along one or more substantially circular trajectories in order to reach the different positions.

9. The method according to any one of claims 1 to 8, characterized in that the measurements are carried out with at least partial overlap along the wavefront.

10. The method according to any one of claims 1 to 9, characterized in that the wavefront sensor(s) is/are pivotable around one axis or two different axes, wherein, in the case of two axes, the axes are oriented preferably at a right angle with respect to one another and/or preferably intersect.

11. The method according to claim 1, characterized in that the wavefront sensor(s) is/are aligned via a controller of a control circuit, in such a manner that a focal point of the wavefront, generated by means of a lens of a wavefront sensor, lies on an optical axis of the lens, wherein the local gradient of the wavefront is preferably derived from the control signals generated for the alignment of the wavefront sensor(s).

12. The method according to any one of claims 1 to 10, characterized in that an optical system generating the wavefront is rotated around an optical axis for the relative positioning of the wavefront with respect to the wavefront sensor(s).

13. The method according to any one of claims 1 to 10, characterized in that one or more wavefront sensors suspended at a suspension point are set in oscillating motion around the suspension point in order to reach the different positions.

14. The method according to any one of claims 1 to 10, characterized in that a plurality of wavefront sensors are arranged on a carrier, wherein preferably the wavefront sensors can be tilted relative to the carrier around at least one axis and preferably shifted relative to the carrier.

15. The method according to any one of claims 1 to 10, characterized in that an end of an optical waveguide sweeps the wavefront at least in sections, and light received at the different positions is transmitted by means of the optical waveguide to the light entrance plane of the wavefront sensor(s).

16. The method according to claim 15, characterized in that the optical waveguide is set in scanning motion, preferably along a circular track, by means of a movement device.

17. The method according to any one of claims 1 to 10, characterized in that the wavefront is reflected via at least one mirror onto the wavefront sensor(s), wherein the mirror is pivoted around one axis or two axes for the measurement at the different positions.

18. An apparatus for measuring a curved wavefront using at least one wavefront sensor, in particular for carrying out the method according to any one of claims 1 to 17, wherein a plurality of measurements are carried out at different positions along the wavefront using at least one wavefront sensor for the determination of a local gradient of the wavefront at the different positions, characterized in that, for carrying out the plurality of measurements, the wavefront sensor(s) can be positioned with substantially tangential alignment of a light entrance plane of the wavefront sensor(s) with the curved wavefront.

Description

[0054] FIGS. 3 and 4 show, in diagrammatic representations, an embodiment example of the method according to the invention for measuring a curved wavefront A, wherein a Shack-Hartmann sensor is used as wavefront sensor, and a spherical wavefront A is measured. For the delimitation of the maximum local gradient tan(.sub.max) of the wavefront A, the entire spherical wavefront A is scanned at a certain distance R along a circular trajectory B at specific points 1 to n. Here, the course of the scanning trajectory Bis represented by a dotted line. Ultimately, a predetermined area of the wavefront A is sensed by individual measurements which are represented by crosshatched areas C. All the individual measurements are recorded along the scanning trajectory B. The area C corresponds to the acquired area of the individual wavefront sensor at a point in time.

[0055] FIG. 4 shows the tangential alignment of the wavefront sensor with respect to the wavefront A. The individual positions or measurement points can be selected so that the individual wavefront images overlap. The entire wavefront is assembled from the sum of the individual wavefronts 1 to n, see FIG. 3. The assembly of the wavefront is carried out by so-called wavefront stitching. The shift displacement S in FIG. 4 here determines the overlap area, by which the precision of the measurement can be influenced. The individual measurements are subsequently imaged on a spherical surface using an algorithm.

[0056] Based on a maximum acceptable local gradient tan(.sub.max) of the wavefront, the following equation must be satisfied:

[00003]$\tan \left({}_{\max }\right)\frac{d_k}{R}$

[0057] In the case of a maximum acceptable wavefront gradient, it is possible to derive therefrom the necessary distance R, the associated wavefront area, and the number of measurements necessary for a complete wavefront image.

[0058] FIG. 5 shows an additional embodiment example in a diagrammatic representation, wherein this relates to a special case in which the sensor consists of a single lens with detector. For this purpose, a commercial lens array can naturally also be used, in which all the other lenses except one are ignored. This sensor is guided along a predetermined scanning trajectory E and is additionally mounted so that it can rotate around two directionsrotation axes C and F. During the measurement process, the inclination of the sensor is controlled via a control circuit so that the focal point lies along the optical axis which corresponds to the detector center. The control signals generated here by the controller of the control circuit for the alignment of the sensor give information on the inclination of the compensated wavefront gradient. Concretely, the wavefront sensor is designed as a 2D detector D which is mounted so that it can rotate around two axes along a scanning trajectory E. During the movement through the scanning trajectory E, the controller attempts to keep the focal point G in the center of the detector D. The control variables generated in the process are proportional to the wavefront gradient. A designates the lens and B designates a wavefront section.

[0059] FIG. 6 shows an additional embodiment example of the invention in a diagrammatic representation. Here, the position of a test optical system is fixed, and a wavefront sensor is moved along a circular track by pivoting around an axis A1a. in addition, degrees of translation freedom are provided parallel to the optical axis and parallel to the axis A1a. Depending on the position of the circular track, the sensor is pivoted around an additional axis A2a, in order to be oriented tangentially with respect to the wavefront. The area acquired at a point in time by the wavefront sensor is designated S.

[0060] Alternatively, it is also conceivable to use only two degrees of rotational freedom, wherein the associated rotation axes intersect. An additional variant of this embodiment is described in FIG. 7.

[0061] FIG. 7 shows an embodiment example of the invention in which the test optical system is mounted so that it can rotate around an axis A1b. By an additional pivotability of the wavefront sensor S around an axis A2b, the complete wavefront can be scanned. Both the axis A2b according to FIG. 7 and the axis A1a according to FIG. 6 run through a focus of the wavefront, which is generated by the test optical system. The tangential alignment with respect to a spherical wavefront is given by the twofold rotatability of the sensor S according to FIG. 7. In addition, the sensor S according to FIG. 7 can also be moved by translation.

[0062] FIG. 8 shows an additional embodiment example of the invention in a diagrammatic representation. Here, the wavefront sensor is suspended on a pendulum. Before the measurement, the pendulum with sensor is deflected, and a starting impulse is transmitted. During the deflection process, images of the wavefront are recorded. An additional possibility consists of the actuation of the pendulum at the suspension point in order to set the pendulum in motion. In FIG. 8, the wavefront sensor is represented at two positions A and B, wherein it continues to move substantially in the shape of a spiral during its deflection process from position A to position B. The sensor is suspended on a cardan joint C which is coupled to the test optical system D. The scanning trajectory of the sensor is designated E.

[0063] In FIGS. 9 and 10, an additional embodiment example of the invention is represented, wherein a plurality of wavefront sensors A are here attached to a carrier B. Thereby, instead of a single wavefront sensor, a sensor array is formed, which consists of an arrangement of a plurality of wavefront sensors A. The individual sensors A are connected via the carrier B which is used as connection frame or support framework.

[0064] For optimal adjustment to the wavefront to be measured, the individual wavefront sensors A can be mounted on their suspension points on the carrier B in in such a manner that they can substantially be freely positionedrotated and shiftedand adjusted by means of actuators, see FIG. 10. The entire sensor array can be guided for enlarging the measurement range over a predefined scanning trajectory orwhile remaining in the positionthey can take an instantaneous picture of the wavefront. In the latter case, one does without a gap-free acquisition. According to FIG. 10, the individual wavefront sensors A are connected to one another in a tiltable and shiftable manner via a support framework B, so that any wavefront radii R can be measured.

[0065] FIG. 11 shows an additional embodiment example of the invention in a diagrammatic representation. Here, an optical waveguide A is arranged practically as a transmission medium between a wavefront generated by a test optical system F and a detector C. The optical waveguide A is set in oscillation via spatially arranged actuators E, for example voice coil actuators, in such a manner that the start of the optical waveguide A is curved along a circular track or scanning trajectory D. The optical waveguide A sweeps the incident wavefront in a converging area of the light and transfer a segment of the wavefront to an outlet of the optical waveguide A. The outlet is here connected stationarily to a base. At the outlet, a wavefront sensor is arranged. In the case of a Shack-Hartmann sensor, an optical system with a lens B is located at the outlet, which converts the inclination of the wavefront into a displacement of the focal point. In summary, by actuation of the start of the optical waveguide A, the entire wavefront generated by the test optical system F can be sensed, therein in each case a segment of the wavefront is transmitted to the outlet, and an inclination of the wavefront is imaged via a lens system B in a displacement of the focal point. The detector C works according to the Shack-Hartmann principle.

[0066] FIG. 12 shows an additional embodiment example of the invention in a diagrammatic representation. Here, the wavefront generated by means of a test optical system A is projected by a deflection mirror B onto a stationary wavefront sensor C. In order to make the principle understandable, only an inclinability of the pivotable mirror B around one axis is represented in FIG. 12. The inclination around a second axis, which is preferably orthogonal with respect to the drawn-in axis, can be implemented in the context of an additional embodiment example. By actuation of the mirror B, the entire wavefront is pivoted over the area of the wavefront sensor C and sensed spatially. Here it is important that the focal point always lies on the mirror surface, since otherwise a movement of the pivot axis is superposed on the pivoting. In the embodiment example shown here, the optical axis D is effectively quasi deflected by means of the deflection mirror B. The wavefront sensor C is represented by the crosshatched area in FIG. 12 and is fixed at a measurement position. Preferably, two orthogonally arranged scanners or deflection mirrors B reflect the incident wavefront in the direction of the wavefront sensor C. By the movement of the scanners or deflection mirrors B, the wavefront to be measured is guided over the measurement area of the sensor C.

[0067] In a wavefront analysis, the representation of the measured wavefront is often carried out by superposition of individual fundamental modespolynomials such as, for example, the Zernike polynomial, which is referred to as modal analysis. The order of the fundamental mode is here linked directly to the number of necessary sensing pointsindividual measurements. If low-frequency fundamental modes are to be analyzed exclusively spatially in a wavefront measurement, a complete sensing of the entire wavefront is not absolutely necessary. The reconstruction based on non-overlapping, spatially separate partial measurements is thus feasible. This can clearly reduce the time necessary for a measurement in scanning processes, since no continuous partial measurements are necessary. In fact, when a wavefront sensor array is used, for example, according to FIGS. 9 and 10, only a single measurement by a simultaneous recording of all the participating wavefront sensors is necessary in order to reconstruct the entire wavefront with sufficient precision.

[0068] The intensity distribution within the cross section of the wavefront to be measured can clearly vary, depending on the light source used, for example, laser, wherein the maximum intensity can occur, for example, in the beam center, and the minimum intensity can occur in the marginal area. If image sensors are used as detectors, different intensity profiles can be compared by superposition of images recorded with different exposure times or by using image sensors based on multislope integration methodspixels with variable exposure time.

[0069] With regard to additional advantageous designs of the method according to the invention and of the apparatus according to the invention, in order to avoid repetitions, reference is made to the general part of the description as well as to the appended claims.

[0070] Finally, it is explicitly pointed out that the above-described embodiment examples of the teaching according to the invention are used only to explain the claimed teaching without limiting said teaching to the embodiment examples.