Of all methods of particle size analysis determination only microscopy and subsequent image analysis enables accurate, geometrically determined size parameters to be measured. For this reason image analysis is a convenient referee or umpire method against which to compare other techniques. In this study, a series of seven poly(vinyl) chloride (PVC) resins were characterized by optical microscopy and image analysis, sieves, HIAC and Coulter counter. It was not found possible to perform the image analysis measurements without operator intervention with a light pen to separate agglomerates. The PVC particles were far too irregular to enable this task to be performed by erosion and dialation techniques. The errors at 90% confidence associated with the image analysis study were: calibration ± 1.7%, counting statistics ± 1% (max) with a focus and algorithms error which ranged from ½‐3% depending upon the quantity being measured. These numbers gave a total error of ± 2% (ca. one pixel) for equivalent circular diameter (ECD) and ± 4% (ca. two pixels) for object breadth. In general the agreement between the various techniques was quite good suggesting that the object breadth (OB) as measured by sieves was nearly identical to equivalent spherical diameter (ECD) as measured by the HIAC and Coulter counter for the samples investigates. A study of the image analysis data alone confirmed that OB and ECD were nearly identical with ECD running about 6.1 m̈m above OB. Mass resin samples, which are prone to electrostatic charging effects, tended to give slightly higher results in those methods which measured the resin in the dry state (HIAC and sieves). Finally, it should be suggested that many of the classical concepts of resolution and depth of focus which are used to place limits upon the performance of the optical microscope do not necessarily apply to particle size determination by image analysis. If the chord through the particle which describes its diameter can be considered an approximation to a square wave then it is the fundamental frequency of the Fourier components of that square wave that contains the size information. This should be true for microscopic objects which are absorbing of light and non‐retarding in nature. Once this fundamental frequency can be identified then sizing accuracy is dependent chiefly on the signal to noise ratio of the system.

Modern image analysis equipment has now made it possible to obtain detailed intensity profile information about objects imaged under the optical microscope. If the object contrast is generated by light absorption alone then the image profile of the object is a square wave and the size information is contained in the fundamental frequency of the Fourier components of that square wave. The period of the fundamental frequency lies very close to the intensity midpoint of the image profile. As long as the microscope objective numerical aperture (NA) is high enough to pass this fundamental the object can be sized to an accuracy which is chiefly dependent upon the signal to noise ratio of the system and independent of classical notions of microscope resolution. Thus for latex particle metal replicas it was possible to determine the diameter to a precision which was typically on the order of 13% of the classical Sparrow limit of resolution for the objective employed. By sizing the same particle replica with objectives of different NA it was demonstrated that the size obtained was independent of the objective NA used as long as the replica diameter was above the Sparrow limit. This is in accordance with optical theory. About mid‐summer the Goldstein "Zernike" program became available to us through the kindness of Dr. Goldstein. With this program it was possible to model the effect of optical path difference. Unlike particle replicas, most real objects generate object profiles that are a function of refractive index difference and thickness or path difference in addition to object size and transmittance. Although the "Zernike" program can accommodate path differences, it assumes that the object has negligible thickness‐an assumption not merited by most real microscopic objects. Although exact quantitative agreement could not always be obtained with reasonable assumptions, the predictions of the "Zernike" program nevertheless could help to define sample preparation conditions which enabled high accuracy sizing to be performed. This work thus demonstrates that an extremely high degree of accuracy and precision in particle sizing is available from the optical microscope which is independent of classical notions of microscope "resolution". The major requirements are that the objective NA be sufficiently high enough to pass the Fourier components which contain the size information and that features in the image can be identified which contain the size information.

We present an efficient and accurate long-form question-answering platform, dubbed iLFQA (i.e., short for intelligent Long-Form Question Answering). The purpose of iLFQA is to function as a platform which accepts unscripted questions and efficiently produces semantically meaningful, explanatory, and accurate long-form responses. iLFQA consists of a number of modules for zero-shot classification, text retrieval, and text generation to generate answers to questions based on an open-domain knowledge base. iLFQA is unique in the question answering space because it is an example of a deployable and efficient long-form question answering system. Question answering systems exist in many forms, but long-form question answering remains relatively unexplored, and to the best of our knowledge none of the existing long-form question answering systems are shown to be sufficiently efficient to be deployable. We have made the source code and implementation details of iLFQA available for the benefit of researchers and practitioners in this field. With this demonstration, we present iLFQA as an open-domain, deployable, and accurate open-source long-form question answering platform. CCS CONCEPTS• Applied computing → Document management and text processing; • Human-centered computing → Accessibility;

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