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NASA NTRS1991

A contribution to laser range imaging technology

The goal of the project was to develop a methodology for fusion of a Laser Range Imaging Device (LRID) and camera data. Our initial work in the project led to the conclusion that none of the LRID's that were available were sufficiently adequate for this purpose. Thus we spent the time and effort on the development of the new LRID with several novel features which elicit the desired fusion objectives. In what follows, we describe the device developed and built under contract. The Laser Range Imaging Device (LRID) is an instrument which scans a scene using a laser and returns range and reflection intensity data. Such a system would be extremely useful in scene analysis in industry and space applications. The LRID will be eventually implemented on board a mobile robot. The current system has several advantages over some commercially available systems. One improvement is the use of X-Y galvonometer scanning mirrors instead of polygonal mirrors present in some systems. The advantage of the X-Y scanning mirrors is that the mirror system can be programmed to provide adjustable scanning regions. For each mirror there are two controls accessible by the computer. The first is the mirror position and the second is a zoom factor which modifies the amplitude of the position of the parameter. Another advantage of the LRID is the use of a visible low power laser. Some of the commercial systems use a higher intensity invisible laser which causes safety concerns. By using a low power visible laser, not only can one see the beam and avoid direct eye contact, but also the lower intensity reduces the risk of damage to the eye, and no protective eyeware is required.

Defigueiredo, Rui J. P.↗

NASA NTRS2013

What Reliability Engineers Should Know about Space Radiation Effects

Space radiation in space systems present unique failure modes and considerations for reliability engineers. Radiation effects is not a one size fits all field. Threat conditions that must be addressed for a given mission depend on the mission orbital profile, the technologies of parts used in critical functions and on application considerations, such as supply voltages, temperature, duty cycle, and redundancy. In general, the threats that must be addressed are of two types-the cumulative degradation mechanisms of total ionizing dose (TID) and displacement damage (DD). and the prompt responses of components to ionizing particles (protons and heavy ions) falling under the heading of single-event effects. Generally degradation mechanisms behave like wear-out mechanisms on any active components in a system: Total Ionizing Dose (TID) and Displacement Damage: (1) TID affects all active devices over time. Devices can fail either because of parametric shifts that prevent the device from fulfilling its application or due to device failures where the device stops functioning altogether. Since this failure mode varies from part to part and lot to lot, lot qualification testing with sufficient statistics is vital. Displacement damage failures are caused by the displacement of semiconductor atoms from their lattice positions. As with TID, failures can be either parametric or catastrophic, although parametric degradation is more common for displacement damage. Lot testing is critical not just to assure proper device fi.mctionality throughout the mission. It can also suggest remediation strategies when a device fails. This paper will look at these effects on a variety of devices in a variety of applications. This paper will look at these effects on a variety of devices in a variety of applications. (2) On the NEAR mission a functional failure was traced to a PIN diode failure caused by TID induced high leakage currents. NEAR was able to recover from the failure by reversing the current of a nearby Thermal Electric Cooler (turning the TEC into a heater). The elevated temperature caused the PIN diode to anneal and the device to recover. It was by lot qualification testing that NEAR knew the diode would recover when annealed. This paper will look at these effects on a variety of devices in a variety of applications. Single Event Effects (SEE): (1) In contrast to TID and displacement damage, Single Event Effects (SEE) resemble random failures. SEE modes can range from changes in device logic (single-event upset, or SEU). temporary disturbances (single-event transient) to catastrophic effects such as the destructive SEE modes, single-event latchup (SEL). single-event gate rupture (SEGR) and single-event burnout (SEB) (2) The consequences of nondestructive SEE modes such as SEU and SET depend critically on their application--and may range from trivial nuisance errors to catastrophic loss of mission. It is critical not just to ensure that potentially susceptible devices are well characterized for their susceptibility, but also to work with design engineers to understand the implications of each error mode. -For destructive SEE, the predominant risk mitigation strategy is to avoid susceptible parts, or if that is not possible. to avoid conditions under which the part may be susceptible. Destructive SEE mechanisms are often not well understood, and testing is slow and expensive, making rate prediction very challenging. (3) Because the consequences of radiation failure and degradation modes depend so critically on the application as well as the component technology, it is essential that radiation, component. design and system engineers work togetherpreferably starting early in the program to ensure critical applications are addressed in time to optimize the probability of mission success.

DiBari, Rebecca↗

NASA NTRS2016

What Can We Learn From Proton Recoils about Heavy-Ion SEE Sensitivity?

The fact that protons cause single-event effects (SEE) in most devices through production of light-ion recoils has led to attempts to bound heavy-ion SEE susceptibility through use of proton data. Although this may be a viable strategy for some devices and technologies, the data must be analyzed carefully and conservatively to avoid over-optimistic estimates of SEE performance. We examine the constraints that proton test data can impose on heavy-ion SEE susceptibility.

probabilistic risk assessment↗

NASA NTRSDate not supplied

Monocular Ranging for Small Unmanned Aerial Systems in the Far-Field

Recent proliferation of small Unmanned Aerial Systems (sUAS) applications requires onboard collision avoidance systems to mitigate the risk of collision with non-cooperative aircraft and manned aircraft, which may not see sUAS in time to perform an avoidance maneuver. An attractive avenue for onboard collision avoidance is the utilization of machine vision cameras due to their low size, weight and power (SWaP) requirements. In this paper, we characterize the range performance of a machine vision system developed in-house and mounted onto an sUAS. The technique was designed to estimate the performance of a sense-and-avoid system to ensure that the sensing components meet the well-clear requirements for the chosen platform and avoidance strategy. Experimental flight-test data was acquired from test-flights flown along multiple collision geometries for two intruders: a general Aviation (GA) aircraft and a fixed-wing sUAS. The ownship and both intruders were instrumented with inertial navigation systems (INS) recording position and attitude information. The range at first detection, 𝑹𝟎, was extracted from in-flight imagery of head-on collision course geometry synchronized with INS data from both aircraft and ground-truth values extracted from the raw imagery. This initial detection distance, 𝑹𝟎, scales with atmospheric attenuation. Therefore, under clear sky conditions, the derived 𝑹𝟎 value represents the upper bound on the detection range achievable by the test configuration of the detector. Results indicate that the maximum initial detection distance for a 4k resolution action camera fitted with a 41º Field of View (FOV) lens is 2.763 ± 0.037 km for a GA aircraft and 0.881 ± 0.061 km for a fixed-wing sUAS, respectively. The in results this study suggest that a vision-based detect and track system may be analyzed using the sensor characterization and contextualized within aircraft well-clear volumes.

Chester V. Dolph↗

NASA NTRS2005

Equipping an FPGA-Based Mars Rover With an LN-200 IMU

The Mars Exploration Rovers (MER) currently navigating the surface of Mars are outfitted with an advanced stereovision correlation algorithm which allows them to "see" three-dimensionally and autonomously avoid obstac'les in their path. A bottleneck of this system is that it is computationally intense and requires 3 minutes of processing for every correlated image and path choice. Taking advantage of the optimization and reprogrammability of FPGAs, the Mobility Avionics lab has reduced this process to under a second. The lab is demonstrating the advancement with a prototype rover, complete with an LN-200 inertial measurement unit (IMU), which is a flight spare from MER. The LN-200 is a space-grade, six degrees-of-freedom IMU using three fiber-optic gyroscopes and three silicon accelerometers and no moving parts. It has particular power-sequencing needs and communicates with a specialized serial protocol (SDLC over RS-422), requiring specific hardware and software for proper functionality and interfacing with an FPGA. The process of incorporating the LN-200 into the system is described herein.

Zola, Nicholas J.↗

NASA NTRS2017

UAS Integration in the NAS Project: Detect and Avoid Display UNITED Demo

This demo shows the UAS-NAS project's Vigilant Spirit Control Station developed in partnership with the U.S. Air Force Research Lab. Attendees will be able to view encounters and see how the DAA and TCAS II alerting and guidance displays are used to avoid simulated aircraft.

Roberts, Zachary↗

NASA NTRS2017

The Dangers of Parametrics

Building a parametric cost model is hard work. The data is noisy and often does not behave like we want it to. We need statistics to give us an indication of the goodness of our models, but; statistics can be manipulated and mislead. On top of all of that, our own very human biases can lead us astray; causing us to see patterns in the noise and draw false conclusions from the data. Yet, it is the data itself that is the foundation for making better cost estimates and cost models. I believe the mistake we often make is we believe that our models are representative of the data; that our models summarize the experiences, the knowledge, and the stories contained in the data. However, it is the opposite that is true. Our models are but imitations of reality. They give us trends, but not truth. The experiences, the knowledge, and the stories that we need in order to make good cost estimates is bound up in the data. You cannot separate good cost estimating from a knowledge of the historical data. One final thought. It is our attempts to make sense out of the randomness that leads us astray. In order to make progress as cost modelers and cost estimators, we must accept that there are real limitations on our ability to model the past and predict the future. I do not believe we should throw up our hands and say this is the best we can do. Rather, to see real improvement we must first recognize these limitations, avoid the easy but misleading solutions, and seek to find ways to better model the world we live in. I don't have any simple solutions. Perhaps the answers lie in better data or in a totally different approach to simulating how the world works. All I know is that we must do our best to speak truth to ourselves and our customers. Misleading ourselves and our customers will, in the end, result in an inability to have a positive impact on those we serve.

Prince, Frank A.↗

NASA NTRS2017

The Dangers of Parametrics

Prince, Frank A.↗

NASA NTRS2003

Linear Polarization Measurements of Chromospheric Emission Lines

We have used the Zurich Imaging Stokes Polarimeter (ZIMPOL I) with the McMath-Pierce 1.5 m main telescope on Kitt Peak to obtain linear polarization measurements of the off-limb chromosphere with a sensitivity better than 1 x 10(exp -5). We found that the off-disk observations require a combination of good seeing (to show the emission lines) and a clean heliostat (to avoid contamination by scattered light from the Sun's disk). When these conditions were met, we obtained the following principal results: 1. Sometimes self-reversed emission lines of neutral and singly ionized metals showed linear polarization caused by the transverse Zeeman effect or by instrumental cross talk from the longitudinal Zeeman effect in chromospheric magnetic fields. Otherwise, these lines tended to depolarize the scattered continuum radiation by amounts that ranged up to 0.2%. 2. Lines previously known to show scattering polarization just inside the limb (such as the Na I lambda5889 D2 and the He I lambda5876 D3 lines) showed even more polarization above the Sun's limb, with values approaching 0.7%. 3. The O I triplet at lambda7772, lambda7774, and lambda7775 showed a range of polarizations. The lambda7775 line, whose maximum intrinsic polarizability, P(sub max), is less than 1%, revealed mainly Zeeman contributions from chromospheric magnetic fields. However, the more sensitive lambda7772 (P(sub max) = 19%) and lambda7774 (P(sub max) = 29%) lines had relatively strong scattering polarizations of approximately 0.3% in addition to their Zeeman polarizations. At times of good seeing, the polarization spectra resolve into fine structures that seem to be chromospheric spicules.

Sheeley, N. R., Jr.↗

NASA NTRS2017

Recent Radiation Test Results for Trench Power MOSFETs

Single-event effect (SEE) radiation test results are presented for various trench-gate power MOSFETs. The heavy-ion response of the first (and only) radiation-hardened trench-gate power MOSFET is evaluated: the manufacturer SEE response curve is verified and importantly, no localized dosing effects are measured, distinguishing it from other, non-hardened trench-gate power MOSFETs. Evaluations are made of n-type commercial and both n- and p-type automotive grade trench-gate device using ions comparable to of those on the low linear energy transfer (LET) side of the iron knee of the galactic cosmic ray spectrum, to explore suitability of these parts for missions with higher risk tolerance and shorter duration, such as CubeSats. Part-to-part variability of SEE threshold suggests testing with larger sample sizes and applying more aggressive derating to avoid on-orbit failures. The n-type devices yielded expected localized dosing effects including when irradiated in an unbiased (0-V) configuration, adding to the challenge of inserting these parts into space flight missions.

Schottky Diodes↗

DOE OSTI2022

Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data

We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ([Formula: see text]) waveform misfit of one is achieved, and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.

Geochemistry & Geophysics↗

NASA NTRS2005

Radar Evaluation of Optical Cloud Constraints to Space Launch Operations

Weather constraints to launching space vehicles are designed to prevent loss of the vehicle or mission due to weather hazards (See, e.g., Ref 1). Constraints include Lightning Launch Commit Criteria (LLCC) designed to avoid natural and triggered lightning. The LLCC currently in use at most American launch sites including the Eastern Range and Kennedy Space Center require the Launch Weather Officer to determine the height of cloud bases and tops, the location of cloud edges, and cloud transparency. The preferred method of making these determinations is visual observation, but when that isn't possible due to darkness or obscured vision, it is permissible to use radar. This note examines the relationship between visual and radar observations in three ways: A theoretical consideration of the relationship between radar reflectivity and optical transparency. An observational study relating radar reflectivity to cloud edge determined from in-situ measurements of cloud particle concentrations that determine the visible cloud edge. An observational study relating standard radar products to anvil cloud transparency. It is shown that these three approaches yield results consistent with each other and with the radar threshold specified in Reference 2 for LLCC evaluation.

Merceret, Francis J.↗

NASA NTRS2017

Packaging Technology for Dielectric-Coating-Less Heavy Ion Radiation Testing of High-Voltage (HV) Electronic Parts

Testing high voltage (HV) electronic parts (greater than 300 V) for sudden event effects (SEE) caused by cosmic rays in the space environment, consisting of energetic heavy-ions, and neutron radiation in the upper atmosphere is a crucial step towards using these parts in spacecraft and aircraft. Due to the nature of cosmic radiation and neutrons, electronic parts are tested for SEE without any packaging and/or shielding over the top of the device. In the case of commercial HV parts, the top of the packaging is etched off and then a thin dielectric coating is placed over the part in order to avoid electrical arcing between the device surface and wire bonds and other components. Even though the effects of the thin dielectric layer on SEE testing can be accounted for, the dielectric layer significantly hinders post testing failure analysis. Replicating the test capability of state-of-the-art packaging while eliminating the need for post radiation test processing of the die surface (that obscures failure analysis) is the goal. To that end, a new packaging concept for HV parts has been developed that requires no dielectric coating over the part. Testing of prototype packages used with Schottky diodes (rated at 1200V) has shown no electrical arcing during testing and leakage currents during reverse bias testing are within the manufactures specifications.

High Voltage↗

NASA NTRS2005

Recommendations for Sense and Avoid Policy Compliance

Since unmanned aircraft do not have a human on board, they need to have a sense and avoid capability that provides an "equivalent level of safety" (ELOS) to manned aircraft. The question then becomes - is sense and avoid ELOS for unmanned aircraft adequate to satisfy the requirements of 14 CFR 91.113? Access 5 has proposed a definition of sense and avoid, but the question remains as to whether any sense and avoid system can comply with 14 CFR 91.113 as currently written. The Access 5 definition of sense and avoid ELOS allows for the development of a sense and avoid system for unmanned aircraft that would comply with 14 CFR 91.113. Compliance is based on sensing and avoiding other traffic at an equivalent level of safety for collision avoidance, as manned aircraft. No changes to Part 91 are necessary, with the possible exception of changing "see" to "sense," or obtaining an interpretation from the FAA General Counsel that "sense" is equivalent to "see."

Source record↗

NASA NTRS2015

Use of Proton SEE Data as a Proxy for Bounding Heavy-Ion SEE Susceptibility

Although heavy-ion single-event effects (SEE) pose serious threats to semiconductor devices in space, many missions face difficulties testing such devices at heavy-ion accelerators. Low-cost missions often find such testing too costly. Even well funded missions face issues testing commercial off the shelf (COTS) due to packaging and integration. Some missions wish to fly COTS systems with little insight into their components. Heavy-ion testing such parts and systems requires access to expensive and hard-to-access ultra-high energy ion accelerators, or significant system modification. To avoid these problems, some have proposed using recoil ions from high-energy protons as a proxy to bound heavy-ion SEE rates.

reliability estimation↗

DOE OSTI2020

Proposed guidance for preparing and reviewing a molten salt non-power production or utilization facility application

Development of non-power molten salt reactors (MSRs) are under consideration to further establish an MSR experience base, support the requirements of Title 10 of the Code of Federal Regulations (10 CFR) Section 50.43(e), and provide any additional analyses needed for development of a full-scale MSR. Guidance provided in this report is based on MSRs operating with liquid fuel (i.e., fuel dissolved within a molten salt). These reactors, unless owned by the DOE or DOD, will require licensing by the US Nuclear Regulatory Commission (NRC) staff. Standard review plan (SRP) guidance for large light water reactors (LWRs) is available in NUREG-0800, Standard Review Plan for the Review of Safety Analysis Reports for Nuclear Power Plants; Light Water Reactor (LWR) Edition. However, NRC staff observed that NUREG-0800 is very cumbersome to apply to non-power reactors “because of the great differences in complexity and hazards between non-power reactors and nuclear power plants.” Therefore, a program to develop performance-based guidance applicable to non-power reactors was initiated. In 1996, NUREG-1537, Parts 1 and 2, Guidelines for Preparing and Reviewing Applications for the Licensing of Non-Power Reactors, was published. Part 1, the format and content guide, suggests a uniform format for presenting information in non-power reactor applications that is acceptable to the NRC staff, but conformance with the format and content is not required. Part 2, the SRP, ensures the quality and uniformity of the staff review of an application. Unfortunately, the application guidelines and SRP do not provide adequate guidance for all advanced non-LWR technologies and applications. This discrepancy eventually led to the 2012 development of interim staff guidance (ISG) for NUREG-1537, which includes criteria for describing and reviewing aqueous homogeneous reactors (AHRs). Specifically, NUREG-1537 ISG, 2012 expanded the original document to address three areas: 1. updated criteria for heterogeneous non-power reactors, 2. criteria for licensing AHRs, and 3. criteria for licensing a Part 50-licensed isotope production facility. In 2015, the US Department of Energy (DOE) opted to build on the AHR NUREG-1537 ISG experience by performing a gap analysis of the guidance that would be used to license a non-power MSR. MSRs represent one of the advanced non-LWR technologies selected by DOE for development through a multiyear cost share award with Southern Company Services. Under this Advanced Reactor Concepts 2015 (DOE Advanced Reactor Concepts [ARC] 15) award program, the DOE tasked Oak Ridge National Laboratory (ORNL) to evaluate the guidance changes that the NRC may need to consider when licensing an MSR non-power reactor. ORNL staff, with support from Boston Government Services, LLC, focused on five system-related chapters in NUREG-1537 that were considered most relevant to inform the effort that would be required for a non-power MSR applicant. ORNL documented this review in a technical report, ORNL/TM-2018/834, Proposed Guidance for Preparing and Reviewing Molten Salt Non-Power Reactor License Applications (NUREG-1537). The report was subsequently shared with industry and the NRC. The 2018 review was limited in scope, focusing on key system chapters based on the expected significance of each chapter relative to expected differences in addressing advanced non-LWR technologies, specifically non-power MSRs, compared with heterogeneously fueled non-power reactors. In the ORNL report, proposed generic adaptations were suggested for the following NUREG-1537 chapters: Chapter 4, “Reactor Description”; Chapter 5, “Reactor Coolant Systems”; Chapter 6, “Engineered Safety Features”; Chapter 9, “Auxiliary Systems”; Chapter 11, “Radiation Protection Program and Waste Management” The inclusion of Chapter 11 in the previous review effort was intended to provide guidance for categorizing the waste-handling process for an MSR operating with homogenous fuel. The introductions from Parts 1 and 2 of the 2012 NUREG-1537 ISG provide guidance for the application and review of production facilities. After a period of operation, non-power MSRs with homogenous fuel will include gaseous and soluble fission products. The gaseous fission products will be collected and held for decay in an off-gas system. There might also be an initiative to polish or filter the soluble fission products in the fuel salt by some mechanical or chemical means. The treatment and handling of fission products in the non-power MSR fuel salt and the description of this process in the safety analysis report (SAR) must be very precise to avoid the waste treatment facility being construed as a co-located special nuclear material (SNM) fuel cycle facility (see Section 2.3 of this report). Subsequent to the release of ORNL/TM-2018/834, NRC staff expressed a desire to continue the regulatory gap analysis that was begun in that report. This would provide additional clarity and information addressed in certain sections of the original report, while also providing new guidance on certain topics not addressed in the original report. This revision would benefit the NRC staff reviewing applications involving non-power MSR designs and would help developers understand how the NRC staff might approach the review of such applications. The focus of this report is to provide infrastructure support to the NRC staff for the regulatory review of non-power MSRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1995

Integrated helmet mounted display concepts for air combat

A piloted simulation study was conducted in a dome simulator to evaluate several Helmet Mounted Display (HMD) formats developed as part of the NASA High Alpha Technology Program (HATP). The display formats conveyed energy management, spatial orientation, and weapons management information. The HMD format was compared to a generic Heads Up Display (HUD) typical of current operational fighter aircraft. Pilots were tasked to spend as much time in a weapon solution as possible, to have the correct weapon selected for the envelope they were in, and to avoid the adversary's weapon envelope as much as possible. Several different displays were tested individually and simultaneously to see how separate display concepts coexisted. Objective results showed that the ability for the pilot to select the correct weapon for the envelope he was in increased by 50% in a moderate workload condition and 90% in a high workload condition with the HMD format. In the post-test comments pilots generally favored the helmet display formats over the HUD formats with a few instances where pilots preferred a simple numeric readout of the parameter. Short term exposure effects of the HMD on visual acuity were also measured and showed no advers results.

Clark, Joseph W.↗

NASA NTRS2007

Iterative-Transform Phase Retrieval Using Adaptive Diversity

A phase-diverse iterative-transform phase-retrieval algorithm enables high spatial-frequency, high-dynamic-range, image-based wavefront sensing. [The terms phase-diverse, phase retrieval, image-based, and wavefront sensing are defined in the first of the two immediately preceding articles, Broadband Phase Retrieval for Image-Based Wavefront Sensing (GSC-14899-1).] As described below, no prior phase-retrieval algorithm has offered both high dynamic range and the capability to recover high spatial-frequency components. Each of the previously developed image-based phase-retrieval techniques can be classified into one of two categories: iterative transform or parametric. Among the modifications of the original iterative-transform approach has been the introduction of a defocus diversity function (also defined in the cited companion article). Modifications of the original parametric approach have included minimizing alternative objective functions as well as implementing a variety of nonlinear optimization methods. The iterative-transform approach offers the advantage of ability to recover low, middle, and high spatial frequencies, but has disadvantage of having a limited dynamic range to one wavelength or less. In contrast, parametric phase retrieval offers the advantage of high dynamic range, but is poorly suited for recovering higher spatial frequency aberrations. The present phase-diverse iterative transform phase-retrieval algorithm offers both the high-spatial-frequency capability of the iterative-transform approach and the high dynamic range of parametric phase-recovery techniques. In implementation, this is a focus-diverse iterative-transform phaseretrieval algorithm that incorporates an adaptive diversity function, which makes it possible to avoid phase unwrapping while preserving high-spatial-frequency recovery. The algorithm includes an inner and an outer loop (see figure). An initial estimate of phase is used to start the algorithm on the inner loop, wherein multiple intensity images are processed, each using a different defocus value. The processing is done by an iterative-transform method, yielding individual phase estimates corresponding to each image of the defocus-diversity data set. These individual phase estimates are combined in a weighted average to form a new phase estimate, which serves as the initial phase estimate for either the next iteration of the iterative-transform method or, if the maximum number of iterations has been reached, for the next several steps, which constitute the outerloop portion of the algorithm. The details of the next several steps must be omitted here for the sake of brevity. The overall effect of these steps is to adaptively update the diversity defocus values according to recovery of global defocus in the phase estimate. Aberration recovery varies with differing amounts as the amount of diversity defocus is updated in each image; thus, feedback is incorporated into the recovery process. This process is iterated until the global defocus error is driven to zero during the recovery process. The amplitude of aberration may far exceed one wavelength after completion of the inner-loop portion of the algorithm, and the classical iterative transform method does not, by itself, enable recovery of multi-wavelength aberrations. Hence, in the absence of a means of off-loading the multi-wavelength portion of the aberration, the algorithm would produce a wrapped phase map. However, a special aberration-fitting procedure can be applied to the wrapped phase data to transfer at least some portion of the multi-wavelength aberration to the diversity function, wherein the data are treated as known phase values. In this way, a multiwavelength aberration can be recovered incrementally by successively applying the aberration-fitting procedure to intermediate wrapped phase maps. During recovery, as more of the aberration is transferred to the diversity function following successive iterations around the ter loop, the estimated phase ceases to wrap in places where the aberration values become incorporated as part of the diversity function. As a result, as the aberration content is transferred to the diversity function, the phase estimate resembles that of a reference flat.

Dean, Bruce H.↗