Absolute linear-in-k spectrometer designs enabled by freeform optics

Multiconfiguration afocal freeform telescopes

An approach to designing multiconfiguration afocal telescopes is developed and demonstrated. Freeform surfaces are used to maximize the achievable diffraction-limited zoom ratio while staying in a compact volume for a two-position multiconfiguration afocal optical system. The limitations of these systems with three-mirror beam paths are discussed and subsequently overcome by introducing an additional degree of freedom. In a four-mirror beam path system, the goal of a 5x zoom ratio is achieved with a compensated exit pupil and diffraction-limited performance. A significant benefit in optical performance when using freeform surfaces is shown compared to more conventional surface types.

Design method for a small F-number two-material uniform dispersion immersion grating imaging spectrometer

Immersion gratings have high dispersion efficiency and have important application value in miniaturized imaging spectrometers, but its serious dispersion nonlinearity causes difficulties in calibration and image processing, which limits its application range. To solve this, this paper presents a design method for a two-material linear dispersion immersion grating device design method, and a compact small F-number immersion grating spectrometer based on it. First the vector form dispersion equation of the two-material immersion grating is derived and the linear spectral dispersion immersion grating design process is given, then a compact small F-number uniform dispersion imaging spectrometer is given as a design example using the proposed method. The results show that when the operating band of the system is 1590-1675 nm, the spectral resolution is better than 0.25 nm, and F-number can achieve better than 2. Compared with traditional single-material immersion grating imaging spectrometer, the designed imaging spectrometer dispersion linearity is significantly improved. Finally, the influence of prism materials, structure parameters and grating parameters on dispersion nonlinearity is analyzed. Design and analysis results show that the proposed two-material immersion grating device has much better spectral dispersion nonlinearity correction ability, and its design method can provide reference to the compact spectrometer design based on immersion gratings.

Exit pupil quality analysis and optimization in freeform afocal telescope systems

Afocal telescopes are often used as foreoptics to existing imaging systems to allow for application flexibility. To properly combine an afocal telescope with an existing imaging system, the exit pupil of the afocal telescope and the entrance pupil of the imaging system must be coincident. Additionally, the exit pupil of the afocal telescope must be well-formed; that is, it must be the correct size and shape to mitigate pupil-matching challenges. This work introduces processes for designing freeform afocal telescopes with an emphasis on understanding how to analyze and control the exit pupil quality of such systems. The included 3-mirror design examples demonstrate the advantages of using freeform surfaces in afocal systems and quantify the tradeoffs required to improve the exit pupil quality.

A Differential Confocal Sensor for Simultaneous Position and Slope Acquisitions Based on a Zero-Crossing Prediction Algorithm

A new sensor type is proposed to accurately detect the surface profiles of three-dimensional (3D) free-form surfaces. This sensor is based on the single-exposure, zero-crossing method and is used to measure position and angle simultaneously. First, the field intensity distribution in the posterior focal plane of the confocal microscope's objective was modeled accurately. Second, because the camera needs to trigger acquisition when the surface (to be measured) reaches the focal position of the sensor, a zero-crossing prediction method based on a sliding window was proposed. Third, a fast, spatially convergent, peak-extraction algorithm was proposed to improve the accuracy and efficiency of peak extraction. This scheme reduces system installation and adjustment difficulties, and the single-exposure, zero-crossing method achieves high-speed, real-time image acquisitions. The experimental results indicate that the average error of the zero-crossing prediction system was 17.63 nm, the average error of the tilt degree measurement was 0.011° in the range of 0-8°, and the prediction error of the tilt direction measurement was 0.089° in the range of 0-360°. The sensor can measure the slope and can be potentially used for 3D surface precision detection.

Implementation of a null test for freeform optics using a high-definition spatial light modulator

We report the implementation of an interferometric null test using a high-definition spatial light modulator (SLM) as a reconfigurable alternative to a computer-generated hologram. We detail the alignment process chain, including novel techniques using the SLM to project alignment fiducials on the test part. To validate the alignment protocol, we measure a mild off-axis conic with the SLM-based system and cross-validate with conventional interferometry within 30 nm root-mean-square (RMS) surface figure. Finally, we report the null test of a 65 mm clear aperture concave freeform with 91 μm peak-valley sag departure from the base sphere. The measured surface figure of the freeform is within 40 nm RMS compared to the measurement with a commercial metrology instrument.

A design method for direct vision coaxial linear dispersion spectrometers

A spectrometer design method based on the prism-prism-grating (PPG) dispersion module is proposed in this paper to correct the serious nonlinear dispersion that prism and grating spectrometers and other dispersive spectrometers suffer from. First, we determine the criteria for selecting the optical materials of the PPG module by analyzing the dispersion characteristics of prisms and gratings. Second, a loop traversal algorithm is used to optimize the system structure parameters after selecting optical materials. Next, the direct vision coaxial condition of the PPG module is derived according to basic optical principles and the geometrical relationship between optical elements. Then, the dispersion equation of the PPG module is used to establish the spectral linearity index of the system. Finally, combined with the design index, the structural parameters of the PPG module to meet the linear dispersion requirements are determined. A direct vision coaxial linear dispersion spectrometer is designed and realized under the condition that the working band is 400-990 nm, the deviation angle and offset of the emitted ray with a central wavelength of 695 nm with respect to the optical axis are 0, and the dispersion angle is not less than 15°. The results simulated by ZEMAX show that the actual simulation results are consistent with the theoretical calculation results, the spectral resolution of the spectrometer is less than 1.5 nm, and the spectral smile and keystone are less than 3.89% pixels. In the discussion section, the influences of the dispersion ability of optical materials and the incident angles of prisms and gratings on the spectral dispersion linearity of the PPG module are analyzed and studied. The universality of the spectrometer design method developed in this paper is discussed, and its universality is simulated and verified in the 1000-1600 nm and 1600-2200 nm bands. In addition, some advantages compared with other dispersion structures are analyzed.

Design Method of Freeform Off-Axis Multi-Mirror Optical Systems

A data point calculation method that does not require the use of Fermat′s principle and a simple and general design method of starting points of freeform off-axis multi-mirror optical systems are proposed in this paper, which aim to promote the realization of high-performance reflective systems containing freeform surfaces. Taking a planar system and the required parameters as the input, a good starting point for a freeform off-axis multi-mirror system can be automatically obtained using the proposed method. The design of a freeform off-axis five-mirror system with a low F-number is taken as an example to show the effectiveness of the proposed method. The method can also be used for the design of freeform reflective systems with other numbers of mirrors.

Automatic design method of starting points of freeform off-axis reflective imaging systems of small volume

For off-axis reflective systems, there is no effective method that can obtain a small-volume starting point automatically. Reducing system volume using the optimization method is usually a difficult and cumbersome process, which usually takes the designer a long time. This paper proposes a method of designing small-volume starting points of freeform off-axis reflective imaging systems, which does not require human involvement after inputting a planar system, specifications and constraints. In the design example presented in this paper, it took only about ten minutes to obtain a small-volume starting point. The starting point obtained by this method makes the optimization process easier, takes less time of designers and more likely to succeed. In the design example, it is also demonstrated that the method has the ability of establishing small-volume starting points with different specifications, which can be used to quickly estimate the minimum volumes that systems with different specifications can achieve and provide guidance for determination of specifications and optimization.

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.

Spectral fusing Gabor domain optical coherence microscopy based on FPGA processing

High-resolution imaging using high numerical aperture imaging optics is commonly known to cause a narrow depth of focus, which limits the depth of field in optical coherence tomography (OCT). To achieve semi-invariant high resolution in all directions, Gabor domain optical coherence microscopy (GD-OCM) combines the in-focus regions of multiple cross-sectional images that are acquired while shifting the focal plane of the objective lens. As a result, GD-OCM requires additional processes for in-focus extraction and fusion, leading to longer processing times, as compared with conventional frequency domain OCT (FD-OCT). We previously proposed a method of spectral domain Gabor fusion that has been proven to improve the processing speed of GD-OCM. To investigate the full potential of the spectral domain Gabor fusion technique, we present the implementation of the spectral domain Gabor fusion algorithm using field programmable gate arrays (FPGAs) in a spectral acquisition hardware device. All filtering processes are now performed in an acquisition device as opposed to the post-processing of the original GD-OCM, which reduces the amount of data transfer between the image acquisition device and the processing host. To clearly demonstrate the imaging performance of the implemented system, we performed GD-OCM imaging of a stack of polymeric tapes. GD-OCM imaging was performed over seven focus zones. The results showed that the processing time for linear wavenumber calibration and spectral Gabor filtering can be improved with FPGA implementation. The total processing time was improved by about 35%.

Improved correction by freeform surfaces in prism spectrometer concepts

The correction of spatial resolution and distortion in imaging spectrometer systems is of great importance due to their significant impact on efficiency and quality. In this study, we analyze the corrective power of freeforms added at different positions in various spectrometer systems for high-performance requirements. The results show that the combination of a freeform prism and a second freeform close to the image has the best correction of distortion while preserving spot size.

Linear-in-wavenumber actively-mode-locked wavelength-swept laser

We report on an akinetic actively-mode-locked wavelength-swept laser (ASL) with a sweep that is highly linear in wavenumber. By tailoring the drive waveform of the intracavity modulator, the wavenumber sweep was further linearized to enable high fidelity frequency-domain interferometric ranging without resampling of the acquired data. Used for catheter-based optical coherence tomography, the ASL showed comparable imaging performance to a state-of-the-art polygon-based wavelength-swept source at a matching sweep rate of 103.6 kHz, a duty cycle of 95%, and a bandwidth of 100 nm, centered at 1330 nm.

Cascade optical coherence tomography (C-OCT)

Significant advances for optical systems in terms of both performance and packaging are enabled by freeform optical components. Yet, surface form metrology for freeform optics remains a challenge. We developed and investigated a point-cloud cascade optical coherence tomography (C-OCT) technique to address this metrology challenge. The mathematical framework for the working principle of C-OCT is presented. A novel detection scheme is developed to enable high-speed measurements. Experimental results validate the C-OCT technique with the prototype setup demonstrating single-point precision of ±26 nm (∼λ/24 at the He-Ne wavelength), paving the way towards full surface measurements on freeform optical components.