Reconfigurable freeform optical systems enable greatly enhanced imaging and focusing performance within nonsymmetric, compact, and ergonomic form factors. In this paper, several improvements are presented for the design, test, and data analysis with these systems. Specific improvements include definition of a modal G and C vector basis set based on Chebyshev polynomials for the design and analysis of non-circular optical systems. This framework is then incorporated into a parametric optimization process and tested with the Tomographic Ionized-carbon Mapping Experiment (TIME), a reconfigurable optical system. Beyond design, a reconfigurable deflectometry system enhances metrology to measure a fast, f/1.26 convex optic as well as an Alvarez lens. Further improvements in an infrared deflectometry system show accuracy around λ/10 of the notoriously difficult low-order power. Working together, the mathematical vector polynomial set, the programmatic optical design approach, and various deflectometry-based optical testing technologies enable more flexible and optimal utilization of freeform optical components and design configurations.
Rectangular pupils are employed in many optical applications such as lasers and anamorphic optics, as well as for detection and metrology systems such as some Shack−Hartmann wavefront sensors and deflectometry systems. For optical fabrication, testing, and analysis in the rectangular domain, it is important to have a well-defined set of polynomials that are orthonormal over a rectangular pupil. Since we often measure the gradient of a wavefront or surface, it is necessary to have a polynomial set that is orthogonal over a rectangular pupil in the vector domain as well. We derive curl (called C) polynomials based on two-dimensional (2-D) versions of Chebyshev polynomials of the first kind. Previous work derived a set of polynomials (called G polynomials) that are obtained from the gradients of the 2-D Chebyshev polynomials. We show how the two sets together can be used as a complete representation of any vector data in the rectangular domain. The curl polynomials themselves or the complete set of G and C polynomials has many interesting applications. Two of those applications shown are systematic error analysis and correction in deflectometry systems and mapping imaging distortion.
Dark field illumination (DFI) is an elegant inspection technique sometimes used to detect particles on a specular surface. However, traditional DFI struggles with repeatability, limiting its applications in automated inspection. We present an improvement to DFI by introducing a modulated dark field illumination (MDFI) that utilizes the phase rather than the intensity in the detection of defects. For modulated dark field illumination (MDFI), the phase-based information is independent from the reflectance of the surface, but has a higher sensitivity to the light scattered from a defect than DFI. As a result, we obtain a robust computational image process method that is insensitive to the environment and provides clearly defined defect information. In order to extend the application to industry, the instantaneous MDFI systems were developed and validated.
Dark-field illumination is a simple yet elegant imaging technique that can be used to detect the presence of particles on a specular surface. However, the sensitivity of dark-field illumination to initial conditions affects its repeatability. This is problematic in cases where automation is desired. We present an improvement to the current method of using a modulation field that relies on phase calculations rather than intensity. As a result, we obtain a computational method that is insensitive to noise and provides clearly defined particle information, allowing a global threshold to be set for autonomous measurement purposes. After introducing the theory behind our method, we present experimental results for various scenarios and compare them to those obtained using the dark-field approach.
A new data processing method based on orthonormal rectangular gradient polynomials is introduced in this work. This methodology is capable of effectively reconstructing surfaces or wavefronts with data obtained from deflectometry systems, especially during fabrication and metrology of high resolution and freeform surfaces. First, we derived a complete and computationally efficient vector polynomial set, called G polynomials. These polynomials are obtained from gradients of Chebyshev polynomials of the first kind – a basis set with many qualities that are useful for modal fitting. In our approach both the scalar and vector polynomials, that are defined and manipulated easily, have a straightforward relationship due to which the polynomial coefficients of both sets are the same. This makes conversion between the two sets highly convenient. Another powerful attribute of this technique is the ability to quickly generate a very large number of polynomial terms, with high numerical efficiency. Since tens of thousands of polynomials can be generated, mid-to-high spatial frequencies of surfaces can be reconstructed from high-resolution metrology data. We will establish the strengths of our approach with examples involving simulations as well as real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.
Deflectometry is a metrology method able to measure large surface slope ranges that can achieve surface reconstruction accuracy similar to interferometry, making it ideal for freeform metrology. While it is a non-null method, deflectometry previously required a precise model of the unit under test to accurately reconstruct the surface. However, there are times when no such model exists, such as during the grinding phase of an optic. We developed a model-free iterative data processing technique which provides improved deflectometry surface reconstruction of optics when the correct surface model is unknown. The new method iteratively reconstructs the optical surface, leading to a reduction in error in the final reconstructed surface. Software simulations measuring the theoretical performance limitations of the model-free processing technique as well as a real-world test characterizing actual performance were performed. The method was implemented in a deflectometry system and a highly freeform surface was measured and reconstructed using both the iterative technique and a traditional non-iterative technique. The results were compared to a commercial interferometric measurement of the optic. The reconstructed surface departure from interferometric results was reduced from 44.39 μm RMS with traditional non-iterative deflectometry down to 5.20 μm RMS with the model-free technique reported.
Dynamic metrology holds the key to overcoming several challenging limitations of conventional optical metrology, especially with regards to precision freeform optical elements. We present two dynamic metrology systems: 1) adaptive interferometric null testing; and 2) instantaneous phase shifting deflectometry, along with an overview of a gradient data processing and surface reconstruction technique. The adaptive null testing method, utilizing a deformable mirror, adopts a stochastic parallel gradient descent search algorithm in order to dynamically create a null testing condition for unknown freeform optics. The single-shot deflectometry system implemented on an iPhone uses a multiplexed display pattern to enable dynamic measurements of time-varying optical components or optics in vibration. Experimental data, measurement accuracy / precision, and data processing algorithms are discussed.
Freeform optics provide excellent performance for a wide variety of applications. However, obtaining an accurate freeform surface measurement is highly challenging due to its large aspheric/freeform departure. It has been proven that SCOTS (Software Configurable Optical Test System), an advanced deflectometry system developed at the University of Arizona, can measure the departure of a freeform surface from the desired shape with nanometer accuracy. Here, a new data processing technique was used to measure a freeform surface without any prior knowledge of the shape of the surface. Knowing only the geometry of one point on the test surface, this method can take a blind measurement of a freeform surface and arrive at the true surface through iterative construction.
The Giant Magellan Telescope (GMT) primary mirror consists of seven 8.4 m light-weight honeycomb mirrors that are being manufactured at the Richard F. Caris Mirror Lab (RFCML), University of Arizona. In order to manufacture the largest and most aspheric astronomical mirrors various high precision fabrication technologies have been developed, researched and implemented at the RFCML. The unique 8.4 m (in mirror diameter) capacity fabrication facilities are fully equipped with large optical generator (LOG), large polishing machine (LPM), stressed lap, rigid conformal lap (RC lap) and their process simulation/optimization intelligence called MATRIX. While the core capability and key manufacturing technologies have been well demonstrated by completing the first GMT off-axis segment, there have been significant hardware and software level improvements in order to improve and enhance the GMT primary mirror manufacturing efficiency. The new and improved manufacturing technology plays a key role to realize GMT, the next generation extremely large telescope enabling new science and discoveries, with high fabrication efficiency and confidence.
The Software Configurable Optical Testing System (SCOTS) is one of the newest testing methods for large mirror surfaces. The Integrated Ray Tracing (IRT) technique can be applicable to the SCOTS simulation by performing non-sequential ray tracing from the screen to the camera detector in the real scale. Therefore, the radiometry of distorted pattern images are numerically estimated by the IRT simulation module. In this study, we construct an IRT SCOTS simulation model for the Fast Steering Mirror Prototype (FSMP) surface of the Giant Magellan Telescope (GMT). GMT FSMP is an off-axis ellipsoidal concave mirror that is 1064 mm in diameter and has PV 3.1 mm in aspheric departure. The surface error requirement is less than 20 nm rms. The screen is modeled as an array of 1366 by 768 screen pixels of 0.227 mm in pitch size. The screen is considered as a Lambertian scattering surface. The screen and the camera are positioned around 4390 mm away from the mirror and separated by around 132 mm from each other. The light source are scanning lines and sinusoidal patterns generated by 616,050 rays per one screen pixel. Of the initially generated rays, 0.22 % are received by the camera’s detector and contribute to form distorted pattern images. These images are converted to the slope and height maps of the mirror surface. The final result for the height difference between input surface and reconstructed surface was 14.14 nm rms. Additionally, the simulated mirror pattern image was compared with the real SCOTS test for the GMT FSMP. This study shows applicability of using the IRT model to SCOTS simulation with nanometer level numerical accuracy.
The accepted screening technique for colon cancer is white light endoscopy. While most abnormal growths (lesions) are detected by this method, a significant number are missed during colonoscopy, potentially resulting in advanced disease. Missed lesions are often flat and inconspicuous in color. A prototype ultraviolet spectral imager measuring autofluorescence (AF) and reflectance has been developed and applied in a study of 21 fresh human colon surgical specimens. Six excitation wavelengths from 280 to 440 nm and formulaic ratio imaging were utilized to increase lesion contrast and cause neoplasms to appear bright compared to normal tissue. It was found that in the subset of lesions which were most difficult to visualize in standard color photographs [low contrast lesions, (LCLs)] a ratio image (F340/F440) of AF images excited at 340 and 440 nm produced extraordinary images and was effective in about 70% of these difficult cases. Contrast may be due to increased levels of reduced nicotinamide adenine dinucleotide, increased hemoglobin absorption, and reduced signal from submucosal collagen. A second successful ratio image (R480/R555) combined two reflectance images to produce exceptional images especially in particular LCLs where F340/F440 was ineffective. The newly discovered ratio images can potentially improve detection rate in screening with a novel AF colonoscope.
Detection of flat neoplasia is a major challenge in colorectal cancer screening, as missed lesions can lead to the development of an unexpected 'incident' cancer prior to the subsequent endoscopy. The use of a tryptophan-related autofluorescence has been reported to be increased in murine intestinal dysplasia. The emission spectra of cells isolated from human adenocarcinoma and normal mucosa of the colon were studied and showed markedly greater emission intensity from cancerous cells compared to cells obtained from the surrounding normal mucosa. A proto-type multispectral imaging system optimized for ultraviolet macroscopic imaging of tissue was used to obtain autofluorescence images of surgical specimens of colonic neoplasms and normal mucosa after resection. Fluorescence images did not display the expected greater emission from the tumor as compared to the normal mucosa, most probably due to increased optical absorption and scattering in the tumors. Increased fluorescence intensity in neoplasms was observed however, once fluorescence images were corrected using reflectance images. Tryptophan fluorescence alone may be useful in differentiating normal and cancerous cells, while in tissues its autofluorescence image divided by green reflectance may be useful in displaying neoplasms.