Mid-spatial frequency (MSF) texture on optical elements degrade their performance. A Zernike polynomial representation of the wavefront can be used to characterize the mid-spatial frequency and predict the optical performance. The ability to generate very large orders of Zernike polynomials enables fitting and describing optical wavefronts all the way from low order form errors to mid-spatial frequencies. Based on a filtering aspect of Zernike polynomials, we show how different fabrication signatures affect optical performance differently. We investigate the Strehl ratio and Modulation Transfer Function (MTF) as optical performance metrics for mid-spatial frequency. We then present how the orthogonality properties of Zernike polynomials along with linear systems theory of MTF can provide an effective tool in separating the optical performance degradation due to different mid-spatial frequency texture. We present an example of real mid-spatial frequency texture to examine the error in the approximation of MTF when using linear systems formulation.
Mid-spatial frequency structure on freeform optical elements induces small-angle scatter and affects performance.
Fabrication techniques involved in making freeform surfaces leave tooling marks on the surface due to the sub-aperture
nature of the fabrication process. In recent years, there has been a growing need for specification and characterization of
the mid-spatial frequencies for freeform surfaces. There are a range of methods to consider for representing the midspatial
frequency content: the power spectral density (PSD), the structure function (SF) and a polynomial basis
representation such as Zernike and Forbes Q-polynomials, as examples. In this paper, we investigate a Zernike
polynomial representation for quantifying the mid-spatial frequency content in height maps. We will show fit
coefficients of synthesized and real data sets to Zernike polynomials from low orders to very large orders. We also
illustrate how this polynomial representation captures certain characteristics of the mid-spatial frequency error. The
results are analyzed and compared with Forbes gradient orthogonal polynomials. Finally, limits of Zernike polynomials
for representing mid-spatial frequency content of the surface are discussed.
Mid-spatial frequency structure on an optical surface induces small-angle scatter in the transmitted wavefront. Freeform
surfaces are particularly susceptible to mid-spatial frequency errors due to the sub-aperture nature of the fabrication
processes. Several surface metrology methods that work for freeform surfaces use an indirect principle, reconstructing
the surface shape from measured surface slope data. The integration process in the presence of measurement noise adds a
spatial correlation to the dataset, leading to spurious spatial frequency structure. In this paper, we use the autocorrelation
function to characterize and evaluate this artificial mid-spatial frequency structure on optical surfaces that are
reconstructed by zonal integration methods.
Roughness on the surface of phase-only micro-optical elements limits their performance. An optical vortex phase element was fabricated, using additive lithography, with an optimized process to achieve minimal surface roughness. Shipley S1827 photoresist was used in order to obtain the appropriate additive lithography dynamic range for the desired phase profile. We investigated the effects of both postapplied and postexposure baking processes, bias exposure dose, as well as the effects of surfactant in the developer. We found the resist surface roughness to be a function of both the temperature and the time of the postapplication baking cycles, as well as the developer surfactant content. Based on our findings, an empirical correlation model was constructed to relate the process parameters with surface roughness measured quantities. The maximum roughness of the optical surface, for the optimized process, was reduced to 40 percent of the value for the unoptimized process and the additive lithography useful exposure range was increased by 10 percent.
The roughness on the surface of phase-only micro-optical elements can limit their performance. An optical vortex phase
element was fabricated by using additive lithography with an optimized process to have minimal surface roughness.
Thick photoresist was used in order to obtain the appropriate dynamic range for the desired phase profile. We
investigated the effects of both post applied and post exposure baking processes, as well as the effects of surfactant in the
developer. We found the resist surface roughness to be a function of both the temperature and the time of the respective
bakes, as well as the developer surfactant content.
Laser-induced breakdown spectroscopy (LIBS) is applied to analyze human fingernails using nanosecond laser pulses. Measurements on 45 nail samples are carried out and 14 key species are identified. The elements detected with the present system are: Al, C, Ca, Fe, H, K, Mg, N, Na, O, Si, Sr, Ti as well as CN molecule. Sixty three emission lines have been identified in the spectrum that are dominated by calcium lines. A discriminant function analysis is used to discriminate among different genders and age groups. This analysis demonstrates efficient discrimination among these groups. The mean concentration of each element is compared between different groups. Correlation between concentrations of elements in fingernails is calculated. A strong correlation is found between sodium and potassium while calcium and magnesium levels are inversely correlated. A case report on high levels of sodium and potassium in patients with hyperthyroidism is presented. It is shown that LIBS could be a promising technique for the analysis of nails and therefore identification of health problems.
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