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The tilted wave interferometer has been developed as a fast and accurate instrument for the measurement of aspheric and freeform surfaces. We present a method for increasing its robustness and flexibility. Tilted wave interferometry crucially depends on accurate calibration and any changes to a calibrated setup require, in general, a recalibration. Therefore, we propose a method for simultaneous topography reconstruction and elimination of errors arising from such changes. An approach to identify trends in systematic errors for the complex non-null setup with a large number of blackbox model parameters is worked out. The procedure allows deriving an error removal scheme for nonrotationally symmetric components based on measurements in different rotational positions. The feasibility and benefit of the error elimination method are shown both by simulation methods and dedicated experiments. A significant reduction of systematic errors even in a miscalibrated state is achieved. Hence, recalibrations are avoided and measurement time and flexibility are improved.
In the last decades, spatial light modulators have been intensively used for different applications in optical measurement systems. Today, the elements have high enough resolutions to be used even for simple holographic applications. We generate dynamic holograms with a pixelated spatial light modulator by inscribing multiple holograms. The laser-illuminated holograms microscopically translate the measuring point in the object plane. Due to the minimal different spot positions, the speckle patterns are also subject of change.
By averaging of the intensity field in the camera plane the speckle noise can be reduced and the accuracy of the spot's position measurement is increased. Furthermore, experimental measurements show features of correcting spot deformations due to optical system aberrations like defocus, astigmatism and coma.
A simulation workflow of the method was developed using a combination of a solution of Maxwell's equations with the Monte Carlo method. These simulations showed the principal feasibility of the method.
The method is validated by measurements at reference samples with characterized material properties, locations and sizes of fluorescent regions. It is demonstrated that sufficient signal quality can be obtained for materials with scattering properties comparable to dental enamel while maintaining moderate illumination powers in the milliwatt range. The depth reconstruction is demonstrated for a range of distances and penetration depths of several hundred micrometers.
Recently, we have proposed an interferometric setup with a diffractive zoom-lens that includes two computer generated holograms for this purpose.1 Their surface phases are a combination of a cubic function for the adaption of aberrations and correction terms necessary to compensate substrate-induced errors. With this system based on Alvarez design a variable defocus and astigmatism controlled by a lateral shift of the second element is achieved.
One of the main challenges is the calibration of the system.
We use a black-box model2 recently introduced for a non-null test interferometer, the so called tilted wave interferometer3 (TWI). With it, the calibration data are calculated by solving an inverse problem. The system is divided in the two parts of illumination and imaging optics. By the solution of an inverse problem, we get a set of data, which describes separately the wavefronts of the illumination and imaging optics. The main difference to the TWI is the flexible diffractive element, which can be used in continuous positions. To combine the calibration data of a couple of positions with the exact placement, we designed alignment structures on the hologram. We will show the general functionality of this calibration and first simulation results.
Digital holography for recording of incoherent-object hologram as complex spatial coherence function
Rapid quantitative phase imaging using phase retrieval for optical metrology of phase-shifting masks
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