Formula for a quick tolerance estimate of transmission variation in optical system with scanning pupil is developed. The estimate uses statistics of surface coating degradation due to random errors in layer thickness and refractive index. Example of using the tolerancing procedure on a sample optical system is presented and discussed.
We present a novel approach to tolerancing slope errors of aspheric surfaces in relay optics of typical avionics head-up displays (HUD). In these systems, a beamlet entering the pilot eye occupies only a tiny fraction of HUD entrance pupil/eyebox with a typical diameter of 125mm. Consequently the beam footprint on any HUD optical surface is a small fraction of its clear aperture. This presents challenges to HUD tolerancing which is typically based on parallax (angular difference in line of sight between left and right eyes) analysis. Aspheric surfaces manufactured by sub-aperture grinding/polishing techniques add another source of error – surface slope error. This type of error not only degrades image quality of observed HUD symbology but also leads to its “waviness” and “floating” especially noticeable when a pilot moves his head within the HUD eyebox. The suggested approach allows aspheric surface slope error tolerancing that ensures an acceptable level of symbology “waviness”. A narrow beamlet is traced from a pilot eye position backwards through the HUD optics until it hits the light source. Due to the small beamlet size, slope error of the aspheric surface acts primarily as an overall tilt/wedge that deviates the beam and causes it to shift. The slope error is acceptable when this shift is not resolved by a pilot eye. The beamlet is scanned over entire eyebox and field of view and the slope error tolerance is established for several zones in the aspheric surface clear aperture. The procedure is then repeated for each aspheric surface.
Three different approaches to calculation of internal structure of bokeh image in camera lenses with two aspheric surfaces are analyzed and compared – the transfer function approach, the beam propagation approach and direct raytracing in an optical design software. The transfer function approach is the fastest and provides accurate results when peak-to-valley of mid-spatial frequency phase modulation induced at the lens exit pupil is below λ/10. Aspheric surfaces are shown to contribute to the bokeh structure differently increasing the complexity of bokeh image especially for offaxis bokeh.
We present theoretical, numerical, and experimental analysis of the cause of internal structure in out-of-focus images of point light sources seen in shots taken with camera lenses that incorporate aspheric surfaces. This “bokeh” structure is found to be due to diffraction on the phase grating at the lens exit pupil induced by small-scale undulations (ripples) of aspheric surfaces. We develop a phase-to-intensity transfer function approach which leads to a simple formula for estimating the intensity modulation ratio in the resulting bokeh based on the out-of-focus distance, amplitude, and frequency of surface undulations. Numerical simulations of bokeh image formation are carried out for a parabolic mirror imager and a double Gauss objective. We find that modulation depth in the bokeh structure calculated by light propagation based simulation agrees with theory when the modulation depth is <30%. Bokeh images are shown to be more sensitive to manufacturing artifacts of an aspheric surface than corresponding degradation in the lens modulation transfer function for a sharp focused image. We apply the transfer function approach to the calculation of the bokeh produced by a measured aspheric surface in a built camera lens and find reasonable agreement between the calculated and measured bokeh structure.
We present theoretical, numerical and experimental analysis of the cause of internal structure of bokeh images often seen
in shots taken with camera lenses that incorporate aspheric surfaces. The bokeh structure was shown to closely reflect
characteristics of the asphere manufacturing process, and found to be due to light diffraction on the phase grating
associated with the aspheric surface.
Results of theoretical analysis were confirmed by numerical simulations and experimental photo shots. Bokeh images
were found to be more sensitive to residual manufacturing artifacts of aspheric surface than corresponding degradation in
lens modulation transfer function for a sharp focused image.
A lightweight single-aperture and multi-spectral sensor operating from Visible to LWIR has been designed, manufactured and tested exploiting a Three Mirror Anastigmat (TMA) telescope featuring thin free-form mirrors electroformed from negative masters. Manufacturing complexity is in place only for the master realization, the contribution of which to the sensor cost decreases with the number of replicas. The TMA, suitable for airborne surveillance applications, has F/no. 1.4, focal length 136 mm and field of view 4.3° × 3.1°, and provides two channels, in the MWIR-LWIR and in the visible waveband. The nominal contrast is better than 75% in the visible at 25 cycles/mm. Electroformed 1 mm thick mirrors keep the sensor mass below 3 kg. Stray light and thermo-structural design has been done to comply with airborne conditions.
A method for performing optical beam shaping in the near-field region using diffractive optical elements generated by
Fresnel based Phased Optimised General Error Diffusion algorithm (POGED) was developed and investigated by means
of numerical simulations. POGED was found to deliver significantly higher signal to noise ratio than iterative
Gerchberg-Saxton type algorithm.
High resolution adaptive phase distortion suppression was experimentally demonstrated for laser interferometers using a liquid crystal television as a phase modulator and an opto-electronic feedback loop. The experiments were carried out for both amplitude division and rotational shear types of interferometers. The suggested iterative control algorithm is based solely on interference pattern information. The results of numerical simulations of a high resolution adaptive system based on rotational shear type interferometers show the system's potential for atmospheric turbulence phase distortion suppression.
An adaptive imaging system with a liquid crystal phase modulator having 127 individually addressed hexagonal elements is experimentally studied. The system operation is based on direct optimization of an image quality metric dependent on image plane intensity distribution. For optimization of the image quality metric we applied a modified version of a stochastic perturbation gradient descent algorithm. Experimental results demonstrated the efficiency of the algorithm for high- resolution adaptive wavefront correction in an imaging system. A modification of the algorithm that significantly accelerates algorithm convergence is suggested and studied by numerical simulation.
Image quality metrics that can be obtained optically using coherent optical systems are discussed. Coherent optical
processing to measure these image quality metrics includes several steps: (a) transformation ofthe image plane intensity
distribution into a phase modulation ofthe coherent wave using a liquid crystal television; (b) diffraction of the phase
modulated wave over a specified distance to enhance particular image spatial frequencies; (c) a secondary intensity-phase
transformation; and (d) application of an image quality analyzer based on speckle field statistical properties. We present
experimental results, along with corresponding numerical simulations, that demonstrate the effectiveness ofthese technique
for adaptive correction of phase-distorted extended source images.