Phase retrieval for high-numerical-aperture optical systems

2003 ◽  
Vol 28 (10) ◽  
pp. 801 ◽  
Author(s):  
Bridget M. Hanser ◽  
Mats G. L. Gustafsson ◽  
David A. Agard ◽  
John W. Sedat
Keyword(s):  
Phase Retrieval ◽  
Numerical Aperture ◽  
Optical Systems ◽  
High Numerical Aperture

Analysis of Phase Distribution of Focused Light in High Numerical Aperture Systems

2010 ◽  
Vol 437 ◽  
pp. 616-620
Author(s):  
Alexander Normatov ◽  
Boris Spektor ◽  
Joseph Shamir
Keyword(s):  
Phase Distribution ◽  
Numerical Aperture ◽  
Mathematical Expression ◽  
Optical Systems ◽  
Entrance Pupil ◽  
High Numerical Aperture ◽  
Diffraction Integral ◽  
Quadratic Phase ◽  
The Difference ◽  
Kirchhoff Integral

High numerical aperture focusing is becoming increasingly important for nanotechnology related applications. Rigorous, vector evaluation of the focused field, in such cases, is usually performed using the Richards-Wolf method which is based on the Debye approach. The resulting field is known to have a piecewise quasi planar phase. A corresponding result, produced by a Fresnel-Kirchhoff integral for aplanatic optical systems of medium and low numerical apertures, leads to the well known physical fact that a quadratic phase exists when the entrance pupil is not located at the front focal plane. Yet, the amplitudes produced in both ways are in a good agreement. In this work we investigated the difference, presented above, in a 2D system with the help of the Stratton-Chu diffraction integral. The amplitude obtained by the Stratton-Chu integral was quite similar to the classic results while the phase exhibited a quadratic behavior, with the quadratic coefficient depending on the numerical aperture of the optical system. For lower numerical apertures it approached the result obtained by the Fresnel-Kirchhoff integral while for higher numerical apertures it was approaching the Richards-Wolf result. A mathematical expression for the quadratic coefficient was derived and verified for various values of numerical aperture.

scholarly journals Absolute characterization of high numerical aperture microscope objectives utilizing a dipole scatterer

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Jörg S. Eismann ◽  
Martin Neugebauer ◽  
Klaus Mantel ◽  
Peter Banzer
Keyword(s):  
Scattered Light ◽  
Numerical Aperture ◽  
Main Idea ◽  
Reference Wave ◽  
Optical Systems ◽  
Reference Object ◽  
Focal Volume ◽  
High Numerical Aperture ◽  
Reference Device

AbstractMeasuring the aberrations of optical systems is an essential step in the fabrication of high precision optical components. Such a characterization is usually based on comparing the device under investigation with a calibrated reference object. However, when working at the cutting-edge of technology, it is increasingly difficult to provide an even better or well-known reference device. In this manuscript we present a method for the characterization of high numerical aperture microscope objectives, functioning without the need of calibrated reference optics. The technique constitutes a nanoparticle, acting as a dipole-like scatterer, that is placed in the focal volume of the microscope objective. The light that is scattered by the particle can be measured individually and serves as the reference wave in our system. Utilizing the well-characterized scattered light as nearly perfect reference wave is the main idea behind this manuscript.

scholarly journals Projection methods for high numerical aperture phase retrieval

2021 ◽  
Author(s):  
Hieu Thao Nguyen ◽  
Oleg Soloviev ◽  
D Russell Luke ◽  
Michel Verhaegen
Keyword(s):  
Phase Retrieval ◽  
Numerical Aperture ◽  
Projection Methods ◽  
The Other ◽  
Projection Operators ◽  
Mathematical Framework ◽  
Convergence Criteria ◽  
Projection Algorithms ◽  
High Numerical Aperture ◽  
Retrieval Problem

Abstract We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.

scholarly journals In-Line Analysis of Diffusion Processes in Micro Channels by Long Distance Raman Photometric Measurement Technology—A Proof of Concept Study

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 116
Author(s):  
Julian Deuerling ◽  
Shaun Keck ◽  
Inasya Moelyadi ◽  
Jens-Uwe Repke ◽  
Matthias Rädle
Keyword(s):  
Numerical Aperture ◽  
Spot Size ◽  
Measuring System ◽  
Optical Systems ◽  
Measurement Technology ◽  
Long Distance ◽  
Measuring Point ◽  
Acetone Concentration ◽  
Micro Channels ◽  
Set Up

This work presents a novel method for the non-invasive, in-line monitoring of mixing processes in microchannels using the Raman photometric technique. The measuring set-up distinguishes itself from other works in this field by utilizing recent state-of-the-art customized photon multiplier (CPM) detectors, bypassing the use of a spectrometer. This addresses the limiting factor of integration times by achieving measuring rates of 10 ms. The method was validated using the ternary system of toluene–water–acetone. The optical measuring system consists of two functional units: the coaxial Raman probe optimized for excitation at a laser wavelength of 532 nm and the photometric detector centered around the CPMs. The spot size of the focused laser is a defining factor of the spatial resolution of the set-up. The depth of focus is measured at approx. 85 µm with a spot size of approx. 45 µm, while still maintaining a relatively high numerical aperture of 0.42, the latter of which is also critical for coaxial detection of inelastically scattered photons. The working distance in this set-up is 20 mm. The microchannel is a T-junction mixer with a square cross section of 500 by 500 µm, a hydraulic diameter of 500 µm and 70 mm channel length. The extraction of acetone from toluene into water is tracked at an initial concentration of 25% as a function of flow rate and accordingly residence time. The investigated flow rates ranged from 0.1 mL/min to 0.006 mL/min. The residence times from the T-junction to the measuring point varies from 1.5 to 25 s. At 0.006 mL/min a constant acetone concentration of approx. 12.6% was measured, indicating that the mixing process reached the equilibrium of the system at approx. 12.5%. For prototype benchmarking, comparative measurements were carried out with a commercially available Raman spectrometer (RXN1, Kaiser Optical Systems, Ann Arbor, MI, USA). Count rates of the spectrophotometer surpassed those of the spectrometer by at least one order of magnitude at identical target concentrations and optical power output. The experimental data demonstrate the suitability and potential of the new measuring system to detect locally and time-resolved concentration profiles in moving fluids while avoiding external influence.

scholarly journals Focal Surface Detection of High Numerical Aperture Objective Lens Based on Differential Astigmatic Method

2021 ◽  
Vol 13 (4) ◽  
pp. 1-8
Author(s):  
Jia-Lin Du ◽  
Wei Yan ◽  
Li-Wei Liu ◽  
Fan-Xing Li ◽  
Fu-Ping Peng ◽  
...  
Keyword(s):  
Numerical Aperture ◽  
Objective Lens ◽  
High Numerical Aperture ◽  
Surface Detection ◽  
Focal Surface
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