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In this review paper, we first provide comprehensive tutorials on two classical methods of polygon-based computer-generated holography: the traditional method (also called the fast-Fourier-transform-based method) and the analytical method. Indeed, other modern polygon-based methods build on the idea of the two methods. We will then present some selective methods with recent developments and progress and compare their computational reconstructions in terms of calculation speed and image quality, among other things. Finally, we discuss and propose a fast analytical method called the fast 3D affine transformation method, and based on the method, we present a numerical reconstruction of a computer-generated hologram (CGH) of a 3D surface consisting of 49,272 processed polygons of the face of a real person without the use of graphic processing units; to the best of our knowledge, this represents a state-of-the-art numerical result in polygon-based computed-generated holography. Finally, we also show optical reconstructions of such a CGH and another CGH of the Stanford bunny of 59,996 polygons with 31,724 processed polygons after back-face culling. We hope that this paper will bring out some of the essence of polygon-based computer-generated holography and provide some insights for future research. 

Abstract. The chemical complexity of biomass burning organic aerosol (BBOA) greatlyincreases with photochemical aging in the atmosphere, necessitatingcontrolled laboratory studies to inform field observations. In theseexperiments, BBOA from American white oak (Quercus alba) leaf andheartwood samples was generated in a custom-built emissions and combustionchamber and photochemically aged in a potential aerosol mass (PAM) flowreactor. A thermal desorption aerosol gas chromatograph (TAG) was used inparallel with a high-resolution time-of-flight aerosol mass spectrometer(AMS) to analyze BBOA chemical composition at different levels ofphotochemical aging. Individual compounds were identified and integrated toobtain relative decay rates for key molecules. A recently developedchromatogram binning positive matrix factorization (PMF) technique was usedto obtain mass spectral profiles for factors in TAG BBOA chromatograms,improving analysis efficiency and providing a more complete determination ofunresolved complex mixture (UCM) components. Additionally, the recentlycharacterized TAG decomposition window was used to track molecular fragmentscreated by the decomposition of thermally labile BBOA during sampledesorption. We demonstrate that although most primary (freshly emitted) BBOAcompounds deplete with photochemical aging, certain components eluting withinthe TAG thermal decomposition window are instead enhanced. Specifically, theincreasing trend in the decomposition m∕z 44 signal (CO2+)indicates formation of secondary organic aerosol (SOA) in the PAM reactor.Sources of m∕z 60 (C2H4O2+), typically attributed tofreshly emitted BBOA in AMS field measurements, were also investigated. Fromthe TAG chemical speciation and decomposition window data, we observed adecrease in m∕z 60 with photochemical aging due to the decay ofanhydrosugars (including levoglucosan) and other compounds, as well as anincrease in m∕z 60 due to the formation of thermally labile organic acidswithin the PAM reactor, which decompose during TAG sample desorption. Whenaging both types of BBOA (leaf and heartwood), the AMS data exhibit acombination of these two contributing effects, causing limited change to theoverall m∕z 60 signal. Our observations demonstrate the importance ofchemically speciated data in fully understanding bulk aerosol measurementsprovided by the AMS in both laboratory and field studies. 

Abstract. We present a rapid method for apportioning the sources of atmospheric organic aerosol composition measured by gas chromatography–mass spectrometry methods. Here, we specifically apply this new analysis method to data acquired on a thermal desorption aerosol gas chromatograph (TAG) system. Gas chromatograms are divided by retention time into evenly spaced bins, within which the mass spectra are summed. A previous chromatogram binning method was introduced for the purpose of chromatogram structure deconvolution (e.g., major compound classes) (Zhang et al., 2014). Here we extend the method development for the specific purpose of determining aerosol samples' sources. Chromatogram bins are arranged into an input data matrix for positive matrix factorization (PMF), where the sample number is the row dimension and the mass-spectra-resolved eluting time intervals (bins) are the column dimension. Then two-dimensional PMF can effectively do three-dimensional factorization on the three-dimensional TAG mass spectra data. The retention time shift of the chromatogram is corrected by applying the median values of the different peaks' shifts. Bin width affects chemical resolution but does not affect PMF retrieval of the sources' time variations for low-factor solutions. A bin width smaller than the maximum retention shift among all samples requires retention time shift correction. A six-factor PMF comparison among aerosol mass spectrometry (AMS), TAG binning, and conventional TAG compound integration methods shows that the TAG binning method performs similarly to the integration method. However, the new binning method incorporates the entirety of the data set and requires significantly less pre-processing of the data than conventional single compound identification and integration. In addition, while a fraction of the most oxygenated aerosol does not elute through an underivatized TAG analysis, the TAG binning method does have the ability to achieve molecular level resolution on other bulk aerosol components commonly observed by the AMS.