The freeform optical surfaces are the advanced optical elements being used in the optical systems ranging from the illumination system, head up display and ophthalmic systems. So far the metrology is not well established for freeform surfaces.There are interferometric, profilometry, deflectometry and slope measurement techniques used to measure the freeform surfaces. Due to non-rotationally symmetric nature of freeform surfaces, slope measurement systems like Shack Hartman Sensors (SHS) are being explored for the measurement of freeform wavefronts. The spatial resolution of Shack Hartmann sensor is limited by the size of the lens lets used in the sensor which is typically 100 μm to 200 μm. The self-imaging based sensing uses a periodic structure which can be replicated under collimated illumination at certain distance known as Talbot distance. If there is a wavefront other than collimated light, the deviation in self-imaging pattern is observed, and this deviation can be utilised for wavefront measurements. Being a smaller pitch of the periodic structure, a high resolution data is obtained. In the present study, we have proposed a high resolution system for measurement of freeform surface using self-imaging based technique, which is having advantage of higher spatial data as compared to Shack Hartman Sensor. A simulation study is carried out and demonstrated the improved performance of the proposed sensor as compared to SHS.
Freeform optics is the next generation optics with no rotation symmetry about any axis. The fabrication and metrology of freeform optics are not possible by conventional techniques. Due to non-symmetric nature, it is more critical to align the freeform surface during fabrication and metrology. Fabrication and metrology accuracies of the freeform optics are mainly limited due to alignment errors at all the stages of development process. In this paper, effects of alignment errors on quality of freeform optics during of fabrication and metrology are studied. It is found that alignment errors have significant contribution on quality of freeform optics development. Different types of fiducials and their importance and utilization are discussed. Further, a strategy for effective alignment of freeform optics is proposed.
The subaperture stitching technique requires the registration of freeform subapertures into global coordinate frame before stitching in order to compute entire freeform wavefront. A scanning Shack-Hartman Sensor (SHS) utilizes translation stages to scan the freeform surface in XY plane and measure the slope data of various subapertures. The measured slope data is then integrated using weighted cubic spline (WCSLI) based integration method to compute the phase data. The positioning error during scanning causes misalignments between the measured subapertures and their nominal values. The least square based subaperture stitching methods are not capable to minimize lateral misalignment errors of freeform subapertures and therefore degrade the performance of subaperture stitching process. In this work, we have utilized fiducial added planes for correction of angular and rotation misalignments of an extended cubic phase plate. An intrinsic surface feature (ISF) based registration method is used for lateral misalignment corrections. Gaussian curvature is used as an intrinsic pattern which can be defined as one of the fundamental second order geometric properties of a surface. Any shift in the peaks of the Gaussian curvature of reference and measured subaperture corresponds to lateral misalignments in X and Y directions and need to be minimized before registration of subaperture into global frame of reference. After precise registrations, all the subapertures are stitched with consistent overlapping area by using least square fitting method. A numerical validation of the proposed scheme is carried out which demonstrates the effectiveness of the proposed method to improve the subaperture stitching accuracy.
This paper addresses the challenges and limitations involved in the measurement of steep freeform wavefront by using Shack-Hartmann Sensor (SHS). To estimate the slope errors, Zemax simulation tool is used to design a SHS setup including array of lenslets and detector plane with predefined specifications. In first step, error due to approximation of tilted plane wavefront over curved wavefront is simulated. Plane, tilted, curved and tilted-curved wavefronts are defined using appropriate ray source objects. The centroids of the focal spots of lenslets are calculated based on the detector data obtained by using ray tracing method, which is done by an in-plane scanning aperture for segmented local wavefronts sequentially.The scanning aperture is used to block rays from more than one lenslet array. Centroids from the focus spots are calculated and the slopes are estimated with respect to collimated reference wavefront for each ray trace process. Further, matrix of slope errors is used as an input for MATLAB routines for surface reconstruction and error estimation. Based on the simulation data, it is found that the assumption used in Shack-Hartmann wavefront measurement introduce residual errors. For example a 50 wave peak to valley input and 1.19 mm thick lenslet array can give up to 9 waves of residual form error. However, very thin lenslets can have very less residual error.The effect of shift of focal plane, tilted plane wavefront and curve wavefront during the reconstruction using SHS is reported.
The metrology of freeform wavefront can be performed by the use of a noninterferometric method, such as a Shack–Hartmann sensor (SHS). Detailed experimental investigations employing an SHS as metrology head are presented. The scheme is of nonnull nature where small subapertures are measured using an SHS and stitched to give the full wavefront. For the assessment of complex misalignment errors during the spiral scanning, a library of residual slope errors has been created, which makes the alignment process fast converging for minimizing the scanning errors. A detailed analysis of the effects of slope and positioning error on reproducibility is presented. It is validated by null test where a null diffractive optical element has been used in a Mach–Zehnder configuration for compensating the freeform shape. A freeform optics is measured by both measurement schemes, and the results are in good agreement. Further, the nonnull-based scanning subaperture stitching scheme is also validated by performing measurements on an aspheric surface and compared with the measurements from the interferometric method (Zygo Verifire).
The increased range of manufacturable freeform surfaces offered by the new fabrication techniques is giving
opportunities to incorporate them in the optical systems. However, the success of these fabrication techniques depends
on the capabilities of metrology procedures and a feedback mechanism to CNC machines for optimizing the
manufacturing process. Therefore, a precise and in-situ metrology technique for freeform optics is in demand. Though
all the techniques available for aspheres have been extended for the freeform surfaces by the researchers, but none of the
techniques has yet been incorporated into the manufacturing machine for in-situ measurement. The most obvious reason
is the complexity involved in the optical setups to be integrated in the manufacturing platforms. The Shack-Hartmann
sensor offers the potential to be incorporated into the machine environment due to its vibration insensitivity, compactness
and 3D shape measurement capability from slope data. In the present work, a measurement scheme is reported in which a
scanning Shack-Hartmann Sensor has been employed and used as a metrology tool for measurement of freeform surface
in reflection mode. Simulation studies are conducted for analyzing the stitching accuracy in presence of various
misalignment errors. The proposed scheme is experimentally verified on a freeform surface of cubic phase profile.