Photometric Ratio Research Articles

Front Cover: From atomic physics, to upper‐atmospheric chemistry, to cosmology: A “laser photometric ratio star” to calibrate telescopes at major observatories

From Atoms to the Universe The expansion of our Universe is accelerating, due to dark energy. But the nature of dark energy has been a mystery since its discovery at the end of the past century. In Research Highlight ntls.20220003, Justin Albert, Dmitry Budker and Hossein Sadeghpour provide an overview of how a laser photometric ratio star (a novel light source generated by laser excitation of the Earth's upper-atmospheric sodium layer, which will radiate equally brightly at wavelengths of 589 nm and 820 nm) can help us precisely calibrate telescopes in order to understand the nature of dark energy.

From atomic physics, to upper‐atmospheric chemistry, to cosmology: A “laser photometric ratio star” to calibrate telescopes at major observatories

The expansion of our Universe is accelerating, due to dark energy. But the nature of dark energy has been a mystery since its discovery at the end of the past century. In Research Highlight https://doi.org/10.1002/ntls.20220003 , Justin Albert, Dmitry Budker and Hossein Sadeghpour provide an overview of how a laser photometric ratio star (a novel light source generated by laser excitation of the Earth's upper-atmospheric sodium layer, which will radiate equally brightly at wavelengths of 589 nm and 820 nm) can help us precisely calibrate telescopes in order to understand the nature of dark energy.

A precise photometric ratio via laser excitation of the sodium layer – II. Two-photon excitation using lasers detuned from 589.16 and 819.71 nm resonances

ABSTRACTThis paper is the second in a pair of papers on the topic of the generation of a two-colour artificial star [which we term a laser photometric ratio star (LPRS)] of de-excitation light from neutral sodium atoms in the mesosphere, for use in precision telescopic measurements in astronomy and atmospheric physics, and more specifically for the calibration of measurements of dark energy using type Ia supernovae. The two techniques, respectively, described in both this and the previous paper would each generate an LPRS with a precisely 1:1 ratio of yellow (589/590 nm) photons to near-infrared (819/820 nm) photons produced in the mesosphere. Both techniques would provide novel mechanisms for establishing a spectrophotometric calibration ratio of unprecedented precision, from above most of Earth’s atmosphere, for upcoming telescopic observations across astronomy and atmospheric physics; thus greatly improving the performance of upcoming measurements of dark energy parameters using type Ia supernovae. The technique described in this paper has the advantage of producing a much brighter (specifically, brighter by approximately a factor of 103) LPRS, using lower power (≤30 W average power) lasers, than the technique using a single 500 W average power laser described in the first paper of this pair. However, the technique described here would require polarization filters to be installed into the telescope camera in order to sufficiently remove laser atmospheric Rayleigh backscatter from telescope images, whereas the technique described in the first paper would only require more typical wavelength filters in order to sufficiently remove laser Rayleigh backscatter.

A precise photometric ratio via laser excitation of the sodium layer – I. One-photon excitation using 342.78 nm light

ABSTRACT The largest uncertainty on measurements of dark energy using type Ia supernovae (SNeIa) is presently due to systematics from photometry; specifically to the relative uncertainty on photometry as a function of wavelength in the optical spectrum. We show that a precise constraint on relative photometry between the visible and near-infrared can be achieved at upcoming survey telescopes, such as at the Vera C. Rubin Observatory, via a laser source tuned to the 342.78 nm vacuum excitation wavelength of neutral sodium atoms. Using a high-power laser, this excitation will produce an artificial star, which we term a ‘laser photometric ratio star’ (LPRS) of de-excitation light in the mesosphere at wavelengths in vacuum of 589.16, 589.76, 818.55, and 819.70 nm, with the sum of the numbers of 589.16 and 589.76 nm photons produced by this process equal to the sum of the numbers of 818.55 and 819.70 nm photons, establishing a precise calibration ratio between, for example, the r and $z$ filters of the LSST camera at the Rubin Observatory. This technique can thus provide a novel mechanism for establishing a spectrophotometric calibration ratio of unprecedented precision for upcoming telescopic observations across astronomy and atmospheric physics; thus greatly improving the performance of upcoming measurements of dark energy parameters using type SNeIa. The second paper of this pair describes an alternative technique to achieve a similar, but brighter, LPRS than the technique described in this paper, by using two lasers near resonances at 589.16 and 819.71 nm, rather than the single 342.78 nm on-resonance laser technique described in this paper.

Spectral and microscopic analysis of fulvic acids isolated from marine fish waste and sugarcane bagasse co-compost

Abstract Fulvic acids are highly beneficial molecules promoting several soil functions such as nutrient absorption, metal transportation and improving soil structure. These activities are assisted by their molecular structure upon interaction with soil medium. The present study describes the isolation of fulvic acids (FA) from mature marine fish waste and sugarcane bagasse co-compost using alkaline extraction method and studying its molecular and structural characteristics using spectroscopic and microscopic techniques. UV–visible spectroscopic analysis of fulvic acids revealed presence of absorption peak at 264 nm due to characteristics of double bonds of aromatic or unsaturated compounds. Fluorescence spectroscopic analysis of fulvic acids showed emission (455 nm) and excitation (395 nm) spectrum respectively. The photometric ratio (E4/E6) and fluorescence index (FI) confirmed high humification degree of FA. The low color co-ordinate values (L* and b*) measured by CIELAB ensured good maturity of the FAs present in the co-compost. Especially, Proton NMR spectroscopy detected resonance signals of aliphatic protons (0.82–2.0 ppm) and aromatic proton (7.5 ppm) in the molecular structure of FA. FTIR spectrum identified functional groups such as hydroxyl; aliphatic, amide I and polysaccharide and classified the FA as type II. Stereo microscopic examination visualized presence of light brown crystalline particles. Further, SEM analysis of the FA particles revealed presence of various shapes such as spherical; cubical; flakes and micro-aggregate structures. Therefore, it is concluded that spectroscopic and microscopic tools are reliable techniques to reveal the molecular and structural characteristics of FA isolated from co-compost for usage as an organic fertilizer.

Revisiting Outlier Rejection Approach for Non-Lambertian Photometric Stereo.

Photometric stereo offers a single camera based approach to recover 3D information and has attracted wide range of applications in computer vision. Presence of non-Lambertian reflections in almost all the real-world objects limits the usage of the Lambertian model for surface normal vector estimation. Previous methods proposed to address such non-Lambertian phenomena employ an outlier rejection approach while more recent methods introduce BRDF models which can generate more accurate results. However, results with comparable accuracy can also be achieved by simply filtering the observed intensity values. This paper presents two novel outlier rejection techniques which attempt to identify the data which are more reliable and likely to be Lambertian. In the first technique, observed intensity values with less reliability are automatically eliminated. This reliability is determined by the responses from a newly introduced inter-relationship function. In the second technique, those photometric ratio equations which are less likely to be Lambertian are identified by observing the residue of the equations. By eliminating the data which is unreliable and likely to be non-Lambertian, surface normal vectors are more accurately estimated. Our comparative and reproducible experimental results using both real and synthetic datasets illustrate superior performance over the state-of-the-art methods, which validates our theoretical arguments presented in this paper.

Earth's albedo variations 1998–2014 as measured from ground‐based earthshine observations

AbstractThe Earth's albedo is a fundamental climate parameter for understanding the radiation budget of the atmosphere. It has been traditionally measured not only from space platforms but also from the ground for 16 years from Big Bear Solar Observatory by observing the Moon. The photometric ratio of the dark (earthshine) to the bright (moonshine) sides of the Moon is used to determine nightly anomalies in the terrestrial albedo, with the aim of quantifying sustained monthly, annual, and/or decadal changes. We find two modest decadal scale cycles in the albedo, but with no significant net change over the 16 years of accumulated data. Within the evolution of the two cycles, we find periods of sustained annual increases, followed by comparable sustained decreases in albedo. The evolution of the earthshine albedo is in remarkable agreement with that from the Clouds and the Earth's Radiant Energy System instruments, although each method measures different slices of the Earth's Bond albedo.

Height from photometric ratio with model-based light source selection

In this paper, we present a photometric stereo algorithm for estimating surface height. We follow recent work that uses photometric ratios to obtain a linear formulation relating surface gradients and image intensity. Using smoothed finite difference approximations for the surface gradient, we are able to express surface height recovery as a linear least squares problem that is large but sparse. In order to make the method practically useful, we combine it with a model-based approach that excludes observations which deviate from the assumptions made by the image formation model. Despite its simplicity, we show that our algorithm provides surface height estimates of a high quality even for objects with highly non-Lambertian appearance. We evaluate the method on both synthetic images with ground truth and challenging real images that contain strong specular reflections and cast shadows.

Phase closure retrieval in an infrared-to-visible upconversion interferometer for high resolution astronomical imaging

This paper demonstrates the use of a nonlinear upconversion process to observe an infrared source through a telescope array detecting the interferometric signal in the visible domain. We experimentally demonstrate the possibility to retrieve information on the phase of the object spectrum of an infrared source by using a three-arm upconversion interferometer. We focus our study on the acquisition of phase information of the complex visibility by means of the phase closure technique. In our experimental demonstration, a laboratory binary star with an adjustable photometric ratio is used as a test source. A real time comparison between a standard three-arm interferometer and our new concept using upconversion by sum-frequency generation demonstrates the preservation of phase information which is essential for image reconstruction.

The Radio-to-Submillimeter Flux Density Ratio of Galaxies as a Measure of Redshift

Abstract We re-examine the technique of determining the redshifts of galaxies from the ratio of the submillimeter-to-radio continuum flux densities based on a recently published catalog of $850\, {\mu \mathrm {m}}$ sources. We derived the expected variation of this ratio as a function of redshift incorporating the expected average luminosity and the spectral energy distribution (SED) of dust emission and the radio continuum. We find that the existing data for most of the high redshift ($z \gtrsim 1$) sources correspond to our new calculation. Amongst the well-identified sources, there is none with an index significantly higher than predicted. Sources which have an index lower than predicted are either within the error zone or much lower, the latter presumably having AGN-dominated radio-continuum emission. We find the median redshift to be $\sim 2$, which is consistent with that deduced by previous work ($\sim 3$) within the error. We also discuss the various systematic effects that can affect the accuracy of the redshift estimate. We examine other methods of redshift estimation, like photometric ratio in the submillimeter and locating the peak of the SED in the rest system of the objects. We conclude that while the various methods are helpful in identifying high-redshift objects and making a crude estimate of the redshift, they are not, at present, accurate enough for a detailed study of redshift distribution of the submillimeter galaxies.

Shape from Photometric Ratio and Stereo

Based on the traditional problem formulation, it is difficult to integrate the two important vision cues, i.e., shading and stereo, for shape reconstruction due to conflicting albedo and image projection assumptions. In this research, we propose a novel scheme to integrate shading and stereo. First, by using the photometric ratio, we derive a new SFS (shape from shading) formulation where no albedo is needed for shape reconstruction. Then, we establish a unified framework for the integration of photometric ratio and stereo by employing perspective projection on a parametric surface via minimizing a cost functional which consists of a weighted sum of shading and stereo errors. Simulation results are given to show the performance of our new robust algorithm.

The gravitational lens system Q0957+561 in the ultraviolet

Photometric and polarimetric observations of both images of the gravitationally lensed quasar Q0957+561 (z(sub em) = 1.41) were obtained in the UV in 1993 with the High Speed Photometer on board the Hubble Space Photometer on board the Hubble Space Telescope. The images exhibited no significant polarization in a bandpass centered on 2770 A (observer's frame); p less than or = 3.2 % (2 sigma upper limit) in each image. The ratio of the flux density in image A to that in image B in late 1993 had a constant valuee, 1.021 +/- 0.008, in four different UV bandpass between 1400 A and 3040 A observer's frame). These results are consistent with the prediction of the gravitation lens interpretation that the photometric ratio of the images measured simultaneously should be independent of frequency. Reprocessed archival spectra of the two images obtained between 1981 and 1983 by the International Ultraviolet Explorer (IUE) show that the photometric ratio of A to B varies between 0.96 and 2.0 in the Ly alpha emission line, and between 0.77 and 1.8 in the O VI lambda 1037 emission line (quasar rest frame). The photometric ratio of A to B at any single epoch is often significantly different in the two emission lines. Accepting the system as a gravitational lens implies that in the quasar the flux in the Ly alpha emsisson line can vary independently of the flux in the 0 IV emission line.

Three-dimensional stereo by photometric ratios

We present a novel robust methodology for corresponding a dense set of points on an object surface from photometric values for three-dimensional stereo computation of depth. The methodology utilizes multiple stereo pairs of images, with each stereo pair being taken of the identical scene but under different illumination. With just two stereo pairs of images taken under two different illumination conditions, respectively, a stereo pair of ratio images can be produced, one for the ratio of left-hand images and one for the ratio of right-hand images. We demonstrate how the photometric ratios composing these images can be used for accurate correspondence of object points. Object points having the same photometric ratio with respect to two different illumination conditions constitute a well-defined equivalence class of physical constraints defined by local surface orientation relative to illumination conditions. We formally show that for diffuse reflection the photometric ratio is invariant to varying camera characteristics, surface albedo, and viewpoint and that therefore the same photometric ratio in both images of a stereo pair implies the same equivalence class of physical constraints. The correspondence of photometric ratios along epipolar lines in a stereo pair of images under different illumination conditions is therefore a robust correspondence of equivalent physical constraints, and the determination of depth from stereo can be performed without explicit knowledge of what these corresponding physical constraints actually are. Whereas illumination planning is required, our photometric-based stereo methodology does not require knowledge of illumination conditions in the actual computation of three-dimensional depth and is applicable to perspective views. This technique extends the stereo determination of three-dimensional depth to smooth featureless surfaces without the use of precisely calibrated lighting. We demonstrate experimental depth maps from a dense set of points on smooth objects of known ground-truth shape, determined to within 1% depth accuracy.

A simple turbidimeter for rapid determination of low bacteria concentrations.

A differential photometric ratio system for turbidity measurements is described. The high sensitivity of this instrument permits the measurement of very low densities of bacterial populations suspended in liquid media. The sensitivity is in the range between 104 and 106 cells/ml in natural aquatic environments.