Freeform Metrology Research Articles

Interferometric metrology probe for highly sloped freeform optics.

A wide variety of systems are employed to measure the surface profile of aspheric and freeform optical surfaces. Freeform metrology systems must accurately characterize the full surface under test, which can be difficult with steep surface slopes. Here we present an interferometric surface metrology probe for highly sloped aspheric and freeform optical surfaces. The optical design of this probe allows the measurement of surface slopes up to 50deg without tilting the probe, which simplifies stage design and increases the accuracy of the system. A spectrally controlled light source is used to create a virtual ball in front of the probe tip to measure the surface distance and angle. This system produces a cloud of points, to which Zernike polynomials are fit and used to reconstruct the surface. We will show sensitivity tests and accuracy results.

Freeform digital twin approach to develop the HP 300 freeform verification standard

Inspired by previous experience in freeform metrology practice and industrial needs, the Czech Metrology Institute developed the freeform standard Hyperbolic paraboloid 300 of dimensions 300mm×300mm×160mm with a freeform functional area of approximately 64000mm2. The paper presents a mathematical–metrological approach to finding a suitable strategy for calibrating the freeform standard on a coordinate measuring machine with a tactile probing system. The calibration strategy consists in the development of a freeform digital twin of the standard, i.e. a continuous digital representation of a freeform measured value with associated uncertainty. A procedure to estimate the uncertainty of the coordinate freeform measurement is described, too. After calibration, the Hyperbolic paraboloid 300 standard will become a verification gauge suitable for use as a precision reference in advanced freeform metrology similar to common verification gauges widely used in length metrology.

Precision Measurement of Complex Optics Using a Scanning-Point Multiwavelength Interferometer Operating in the Visible Domain

The growing demands of optical systems have led to increasingly complex aspheres and freeforms. In this paper, an established measurement system in asphere production, which is also a promising approach in high-precision freeform metrology, is presented. It is based on a scanning-point multiwavelength interferometer approach. The scanning principle enables great flexibility, reduces setup time and costs, and has almost no limitations in spherical departure. Due to the absolute measurement capability, the utilized multiwavelength approach is beneficial for segmented, annular, and discrete surfaces, which are common designs of modern applications’ optical elements. The metrology system enables measurements on a nanometer scale on a great variety of apertures—from 1 to 1000 mm. Recently, a new short-coherence multiwavelength interferometer operating in the visible domain has been developed. It enables the high-precision measurement on silicon-coated surfaces, which can be found in space applications and are also commonly used for extreme-ultraviolet (EUV) lithographic setups, which will be used as an example throughout this work. Owing to the large absolute measurement capability, applied grating structures for suppressing infrared light in the EUV process can easily be measured. This paper summarizes the basic working principles of the proposed metrology system, explains the special requirements for different fields of application, highlights the capabilities of the visible multiwavelength approach, and shows the measurement results.

Complex illumination system for fast interferometric measurements

Freeform metrology is an enabling technology for today’s research and advanced manufacturing. The Tilted Wave Interferometer is a full field measurement system for fast and flexible measurements. It is based on an off-axis illumination scheme based on a microlens array. In this contribution, we present a novel illumination system for the tilted wave interferometer, that allows to reduce the measurement time by a factor of four using parallelization based on wavelength multiplexing. Here we present a design solution that utilizes the flexibility of 3D-printing. The microlenses are realized as multi-order diffractive optical elements, providing a high efficiency compared to colorfilter based realizations. To boost the light efficiency of the novel illumination system further, a field lens functionality is added to the system by adding individual micro-prisms to each microlens. The system is manufactured by the use of grayscale two-photon polymerisation.

Give your optical metrology a LIFT

Shack Hartmann (SH) Wavefront Sensing (WFS) brings many advantages that has made it a standard in optical metrology, but it has long been limited by its resolution compared to other solutions, such as interferometry. We will present a new approach to the linearized focal plane technique (LIFT), formerly developed by ONERA, which is based on the combination of standard SH technology with phase retrieval algorithms. Applied on all the spots of the SH wavefront sensor microlens array, it provides information on high spatial frequencies, allows to reconstruct more modes for each microlens and results in a 16-fold improvement (4x in each transverse direction) of the sensor spatial resolution! We will present how we have optimized and validated the LIFT technology for optical metrology. We will share some measurements performed on extremely complex wavefronts. Finally, we will propose an implementation for industrial applications such as manufacturing and will describe some use cases. Benefiting from the same advantages as SH WFS -such as robustness to vibrations and atmospheric turbulence, or the ability to easily work at any wavelength- the LIFT technology presents very promising perspectives for optical and freeform metrology and can advantageously replace, at lower cost and better usability, Fizeau interferometry.

Telephoto-lens-based Optical Differentiation Wavefront Sensor for freeform metrology.

We report an Optical Differentiation Wavefront Sensor based on a telephoto lens system and binary pixelated filters. It provides a five-fold reduction in the system length compared to a 4f system with identical effective focal length. Measurements of phase plates with this system are compared to measurements performed with a commercial low-coherence interferometer. The telephoto-lens-based system can measure wavefronts with accuracy better than λ/10 Root Mean Squared (RMS) at λ=633 nm. Experimental investigation shows that the system has a high tolerance to components alignment errors.

Verification of cascade optical coherence tomography for freeform optics form metrology.

Freeform optical components enable dramatic advances for optical systems in both performance and packaging. Surface form metrology of manufactured freeform optics remains a challenge and an active area of research. Towards addressing this challenge, we previously reported on a novel architecture, cascade optical coherence tomography (C-OCT), which was validated for its ability of high-precision sag measurement at a given point. Here, we demonstrate freeform surface measurements, enabled by the development of a custom optical-relay-based scanning mechanism and a unique high-speed rotation mechanism. Experimental results on a flat mirror demonstrate an RMS flatness of 14 nm (∼λ/44 at the He-Ne wavelength). Measurement on a freeform mirror is achieved with an RMS residual of 69 nm (∼λ/9). The system-level investigations and validation provide the groundwork for advancing C-OCT as a viable freeform metrology technique.

APPLICATION OF RULED SURFACES IN FREEFORM AND GEAR METROLOGY

An application of two ruled surfaces (i.e., surfaces generated by a motion of a straight line), a surface of hyperbolic paraboloid and a tangent surface of a cylindrical helix in freeform and gear metrology is introduced in this paper. Both surfaces have been implemented as the main functional figures in several artefacts – metrological calibration standards intended for testing the freeform capabilities of various measuring technologies (e.g., tactile point-to-point measurement and tactile scanning on coordinate measuring machine, optical scanning, computer tomography). Geometrical and mathematical properties of the surface used are summarised, CAD models of all the developed standards are presented and photos of the manufactured standards are shown.

Development of a concave freeform surface measurement using transverse translation-diverse phase retrieval

Transverse translation-diverse phase retrieval (TTDPR), a ptychographic wavefront-sensing technique, is a viable method for freeform optical surface metrology due to its relatively simple hardware requirements, flexibility, and demonstrated accuracy in other fields. In TTDPR, a subaperture illumination pattern is scanned across an optic under test, and the reflected intensity is gathered on an array detector near focus. A nonlinear optimization algorithm is used to reconstruct the wavefront aberration at the test surface from which we can solve for surface error, using intensity patterns from multiple scan positions. TTDPR is an advantageous method for aspheric and freeform metrology because measurements can be performed without null optics. We report on the development of a concave freeform mirror measurement using this technique. Simulations were performed to test algorithmic performance as a function of various parameters, including detector signal-to-noise ratio and position uncertainty of the illumination, with <λ / 100 root-mean-square (rms) wavefront-sensing error achieved in most cases (λ = 632.8 nm). An experimental measurement is then demonstrated, and results of reconstructed surface form and midspatial frequency error are presented. Surface reconstructions from two disjoint datasets agree to 13-nm rms, or λ / 50 at λ = 632.8 nm.

High-performance optical differentiation wavefront sensing towards freeform metrology.

We report the demonstration of freeform optics metrology with an optical differentiation wavefront sensor that relies on spatially dithered distributions of binary pixels to synthesize a far-field amplitude filter. Analysis of experimental results and comparison with a commercial low-coherence-length interferometer shows that freeform phase plates with different magnitude of wavefront slopes can be accurately characterized. RMS accuracy of ∼ λ/10 and precision of ∼ λ/70 at 633 nm were achieved with pixelated filters having 2.5-µm pixels. Simulations that describe the characterization of a freeform optical component in the presence of photodetection noise and filter nonlinearity demonstrate the robustness of this wavefront-sensing approach for freeform optics characterization.

System design of a single-shot reconfigurable null test using a spatial light modulator for freeform metrology.

We report the simulation of an adaptive interferometric null test using a high-definition phase-only spatial light modulator (SLM) to measure form and mid spatial frequencies of a freeform mirror with a sag departure of 150 μm from its base sphere. A state-of-the-art commercial SLM is modeled as a reconfigurable phase computer generated hologram (CGH) that generates a nulling phase function with close to an order of magnitude higher amplitude than deformable mirrors. The theoretical uncertainty in form measurement arising from pixelation and phase quantization of the SLM is 50.62 nm RMS. The calibration requirements for hardware implementation are detailed.

Weighted spline based integration for reconstruction of freeform wavefront

In the present work, a spline-based integration technique for the reconstruction of a freeform wavefront from the slope data has been implemented. The slope data of a freeform surface contain noise due to their machining process and that introduces reconstruction error. We have proposed a weighted cubic spline based least square integration method (WCSLI) for the faithful reconstruction of a wavefront from noisy slope data. In the proposed method, the measured slope data are fitted into a piecewise polynomial. The fitted coefficients are determined by using a smoothing cubic spline fitting method. The smoothing parameter locally assigns relative weight to the fitted slope data. The fitted slope data are then integrated using the standard least squares technique to reconstruct the freeform wavefront. Simulation studies show the improved result using the proposed technique as compared to the existing cubic spline-based integration (CSLI) and the Southwell methods. The proposed reconstruction method has been experimentally implemented to a subaperture stitching-based measurement of a freeform wavefront using a scanning Shack-Hartmann sensor. The boundary artifacts are minimal in WCSLI which improves the subaperture stitching accuracy and demonstrates an improved Shack-Hartmann sensor for freeform metrology application.