Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope.

Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where "local" refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations.

Experimental investigation in nodal aberration theory (NAT): separation of astigmatic figure error from misalignments in a Cassegrain telescope.

We present simulations and experimental validations for separating astigmatic figure error from misalignments in Nodal Aberration Theory (NAT) with a high-precision Cassegrain telescope. Both the primary mirror figure error and the secondary mirror misalignments induce binodal astigmatism for the telescope systems. The separation of these two aberration factors plays a crucial role in the telescope alignment process. In this study, the figure error of the aspheric primary mirror of the Cassegrain telescope induced by the mirror mounts was measured interferometrically utilizing a computer-generated hologram (CGH). According to the primary mirror figure error, the astigmatic node locations in the image plane were simulated using real raytracing. The center of the nodes was located on the field center, and the nodes were placed symmetrically with respect to the field center in the image plane. The telescope's alignment was performed using the simulation results, and the node locations were measured on a grid of field points interferometrically. Thereafter, secondary mirror misalignments around the coma-free pivot point were introduced into the optical system, and the node's center was shifted from the field center in the image plane as predicted by NAT. The simulations and interferometric field measurements were performed and compared on a grid of field points for the misaligned state in the presence of primary mirror figure error. The experimental results confirm the predictions from NAT. Statistical analysis was also performed to confirm the accuracy and stability of the measurements.

Experimental investigation of binodal astigmatism in nodal aberration theory (NAT) with a Cassegrain telescope system.

We present simulations and an experimental investigation of binodal astigmatism in nodal aberration theory (NAT) for a customized, high-precision Cassegrain telescope system. The telescope system utilizes a five-axis, piezo-actuated flexural mechanism to introduce secondary mirror misalignments and generate aberrations intentionally. The induced aberrations are measured interferometrically and quantified for a grid of field points on the telescope system's image plane. For this purpose, a coma-free pivot point of the secondary mirror was simulated for isolating the binodal astigmatism field response. The separation of the nodes is proportional to the introduced misalignments. A simulation of Fringe Zernike coma and binodal astigmatism was generated using a real ray trace model of the optical system and analyzed to compare to the experimental results. A statistical analysis of the measurements was performed to show the experimental results' accuracy and stability. The experimental results were consistent with the simulations, hence experimentally validating NAT for binodal astigmatism for the first time.

Design of a high-precision, 0.5 m aperture Cassegrain collimator.

We present the realization of a high-precision, 0.5 m aperture size Cassegrain collimator system. The optical design, the optomechanical design, the mirror manufacturing, and the telescope alignment with a performance evaluation are extensively discussed. The optical design of the collimator is based on the Cassegrain telescope design with two aspheric mirrors. An athermalized, high stability optomechanical structure is conceived for the collimator to meet stringent performance requirements. The high-quality mirrors are made of low-expansion Zerodur glass-ceramic and the primary mirror is light-weighted to 63% of its initial weight. The design of a dedicated five-axis flexure mechanism driven by nanopositioner stages to compensate the secondary mirror misalignments is given. Primary and secondary mirrors with aspheric surfaces are manufactured, and their forms are measured by computer-generated holograms with a phase-shifting Fizeau interferometer. The alignment strategy is based on minimizing Fringe Zernike coefficients of wavefront decomposition measured by an autocollimation test setup. The alignment sensitivity and corresponding Fringe Zernike coefficient terms are determined by the ray-tracing software that introduces the intentional misalignments of the secondary mirror. The on-axis alignment of the collimator is performed with the guidance of sensitivity analysis results. The final root-mean-square wavefront error for the collimated beam is measured to be 0.021λ.

Radiation pressure excitation of a low temperature atomic force/magnetic force microscope for imaging in 4-300 K temperature range.

We describe a novel radiation pressure based cantilever excitation method for imaging in dynamic mode atomic force microscopy (AFM) for the first time. Piezo-excitation is the most common method for cantilever excitation, however it may cause spurious resonance peaks. Therefore, the direct excitation of the cantilever plays a crucial role in AFM imaging. A fiber optic interferometer with a 1310 nm laser was used both for the excitation of the cantilever at the resonance and the deflection measurement of the cantilever in a commercial low temperature atomic force microscope/magnetic force microscope (AFM/MFM) from NanoMagnetics Instruments. The laser power was modulated at the cantilever's resonance frequency by a digital Phase Locked Loop (PLL). The laser beam is typically modulated by ∼500 µW, and ∼141.8 nmpp oscillation amplitude is obtained in moderate vacuum levels between 4 and 300 K. We have demonstrated the performance of the radiation pressure excitation in AFM/MFM by imaging atomic steps in graphite, magnetic domains in CoPt multilayers between 4 and 300 K and Abrikosov vortex lattice in BSCCO(2212) single crystal at 4 K for the first time.

Thermal refocusing method for spaceborne high-resolution optical imagers.

We describe the design of a thermal refocusing method for spaceborne high-resolution imagers where Korsch optical design is usually implemented. The secondary mirror is made of aluminum, a high thermal expansion coefficient material, instead of conventional zero-expansion glass ceramics. In this way, the radius of the curvature can be controlled by means of temperature change of the mirror. Change in the radius of curvature also changes the effective focal length of the camera which is used for compensation of the defocus that occurred in space. We show that the 30 µm despace of the secondary mirror in the optical system can be compensated by an ∼10°C temperature change of the mirror while the image quality is maintained.

An ultra-low temperature scanning Hall probe microscope for magnetic imaging below 40 mK.

We describe the design of a low temperature scanning Hall probe microscope (SHPM) for a dilution refrigerator system. A detachable SHPM head with 25.4 mm OD and 200 mm length is integrated at the end of the mixing chamber base plate of the dilution refrigerator insert (Oxford Instruments, Kelvinox MX-400) by means of a dedicated docking station. It is also possible to use this detachable SHPM head with a variable temperature insert (VTI) for 2 K-300 K operations. A microfabricated 1µm size Hall sensor (GaAs/AlGaAs) with integrated scanning tunneling microscopy tip was used for magnetic imaging. The field sensitivity of the Hall sensor was better than 1 mG/√Hz at 1 kHz bandwidth at 4 K. Both the domain structure and topography of LiHoF4, which is a transverse-field Ising model ferromagnet which orders below TC = 1.53 K, were imaged simultaneously below 40 mK.

Design of a self-aligned, wide temperature range (300 mK-300 K) atomic force microscope/magnetic force microscope with 10 nm magnetic force microscope resolution.

We describe the design of a wide temperature range (300 mK-300 K) atomic force microscope/magnetic force microscope with a self-aligned fibre-cantilever mechanism. An alignment chip with alignment groves and a special mechanical design are used to eliminate tedious and time consuming fibre-cantilever alignment procedure for the entire temperature range. A low noise, Michelson fibre interferometer was integrated into the system for measuring deflection of the cantilever. The spectral noise density of the system was measured to be ∼12 fm/√Hz at 4.2 K at 3 mW incident optical power. Abrikosov vortices in BSCCO(2212) single crystal sample and a high density hard disk sample were imaged at 10 nm resolution to demonstrate the performance of the system.