Parallactic Angle Research Articles

Polarization Criterion in Targeted SETI Observation

In this paper, we propose a novel method for distinguishing extraterrestrial intelligence (ETI) signals from radio frequency interference (RFI) by leveraging polarization features. We exploit the sinusoidal variation of the linearly polarized components of Stokes parameters with the parallactic angle as a characteristic signature of ETI signals, while such linearly polarized components remain relatively stable for terrestrial RFI. Typically, a minimum of 4–8 hr of observation time is required to detect these sinusoidal variations. The polarization approach in the search for extraterrestrial intelligence also enables us to study the radio stellar bursts emitted by M-type stars as ancillary science, which is relevant to assessing the habitability of exoplanets. Compared to the frequency drift method, the polarization method effectively reduces the required observation time for signal identification while improving the signal identification process.

Improving pulsar polarization and timing measurements with the Nançay Radio Telescope

Context. Accurate polarimetric calibration of the radio pulse profiles from pulsars is crucial for studying their radiation properties at these wavelengths. Additionally, inaccurate calibration can distort recorded pulse profiles, introducing noise in time of arrival (TOA) data and thus degrading pulsar timing analyses. One method for determining the full polarimetric response of a given telescope is to conduct observations of bright polarized pulsars over wide ranges of parallactic angles, to sample different orientations of their polarization angle and in turn determine the cross-couplings between polarization feeds. Aims. The Nançay decimetric Radio Telescope (NRT) is a 94 m equivalent meridian telescope, capable of tracking a given pulsar for approximately 1 h around transit. The NRT therefore cannot sample wide ranges of parallactic angles when observing a given pulsar, so until late 2019 the polarimetric calibration of 1.4 GHz pulsar observations with the NRT was rudimentary. We therefore aimed to develop a method for improving the calibration of NRT observations, overcoming the above-mentioned limitation. Ultimately, our goal was to improve the quality of NRT pulsar timing, with better calibrated pulsar pulse profiles. Methods. In November 2019, we began conducting regular observations of the bright and highly linearly polarized pulsar PSR J0742−2822, in a special observing mode in which the feed horn rotates by ~180° over the course of the 1 h observation, mimicking wide parallactic angle variations and in principle enabling us to determine the polarimetric response of the NRT at 1.4 GHz. In addition, we assessed the quality of the NRT timing of a selection of millisecond pulsars (MSPs), namely, J1730−2304, J1744−1134, and J1857+0953, with conventional TOAs extracted from total intensity pulse profiles, and TOAs extracted with the Matrix Template Matching (MTM) technique, designed to compensate for putative polarimetric calibration errors. Results. From the analysis of the rotating horn observations of PSR J0742−2822 we could determine the cross-couplings between the polarization feeds and also constrain the Stokes parameters of the noise diode signal, which prior to this work was erroneously assumed to be ideal and was used as the only reference source for the calibration of pulsar observations. The improved polarimetric response of the NRT as determined from these observations was applied to observations of a selection of MSPs with published polarimetric properties. We find that the new polarimetric profiles and polarization position angles are consistent with previous findings, unlike NRT polarimetric results obtained with the previously used method of calibration. The analysis of the timing data shows that the new calibration method improves the quality of the timing, and the MTM method proves very effective at reducing noise from imperfect calibration. For pulsars with sufficient degrees of polarization, the MTM method appears to be the preferred method of extracting TOAs from NRT observations.

Robust analysis of differential Faraday rotation based on interferometric closure observables

Polarization calibration of interferometric observations is a costly procedure and in some cases (e.g., due to limited coverage of paral-lactic angle for the calibrator), it may not be possible to carry out this process. To avoid this worst-case scenario, while extending the possibilities for the exploitation of polarization interferometric observations, the use of a new set of calibration-independent quantities (closure traces) has been proposed. However, these quantities suffer from some degeneracies, so their use in practical situations may be rather limited. In this paper, we explore the use of closure traces on simulated and real observations, showing that (with the proper selection of fitting parameters) it is possible to retrieve information on the source polarization using only closure traces and to constrain spatially resolved polarization. We carried out the first application of closure traces to the brightness modeling of real data, using the ALMA observations of M87 conducted during the April 2017 EHT campaign and quantifying a gradient in the Faraday rotation along the source structure (the M87 jet). This work opens the possibility to apply similar strategies to observations from any kind of interferometer (with a special focus on VLBI), whereby quantities such as the differential rotation measure or the spatially resolved polarization can be retrieved.

Feasibility Study of a W-Band Multibeam Heterodyne Receiver for the Gregorian Focus of the Sardinia Radio Telescope

We report on the feasibility study of a W-band multibeam heterodyne receiver for the Sardinia Radio Telescope (SRT), a general purpose fully steerable 64-m diameter antenna located on the Sardinia island, Italy, managed by INAF (“Istituto Nazionale di Astrofisica,” Italy). The W-band front-end is designed for the telescope Gregorian focal plane and will detect both continuum and molecular spectral lines from astronomical sources and radio emission from the Sun in the 3 mm atmospheric window. The goal specification of the receiver is a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> focal plane array operating in dual-linear polarization with a front-end consisting of feed-horns placed in cascade with waveguide Orthomode Transducers (OMTs) and LNAs (Low Noise Amplifiers) cryogenically cooled at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx $ </tex-math></inline-formula> 20 K. The instantaneous FoV (Field of View) of the telescope is limited by the shaping of the 64-m primary and 7.9-m secondary mirrors. The cryogenic modules are designed to fit in the usable area of the focal plane and provide high-quality beam patterns with high antenna efficiency across the 70 – 116 GHz Radio Frequency (RF) band. The FoV covered by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> array is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.15\times 2.15$ </tex-math></inline-formula> arcmin <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , unfilled, with separation between contiguous elements of 43 arcsec. Dual-sideband separation (2SB) down-conversion mixers are designed to be placed at the cryostat output and arranged in four four-pixel down-conversion modules with 4 – 12 GHz Intermediate Frequency (IF) bands (both Upper Side Band and Lower Side Band selectable for any pixel and polarization). The receiver utilizes a mechanical derotator to track the parallactic angle.

HST/FGS Trigonometric Parallaxes of M-dwarf Eclipsing Binaries

Hubble Space Telescope (HST) Fine Guidance Sensor (FGS) trigonometric parallax observations were obtained to directly determine distances to five nearby M-dwarf/M-dwarf eclipsing binary systems. These systems are intrinsically interesting as benchmark systems for establishing basic physical parameters for low-mass stars, such as luminosity L, and radius R. HST/FGS distances are also one of the few direct checks on Gaia trigonometric parallaxes, given the comparable sensitivity in both magnitude limit and determination of parallactic angles. A spectral energy distribution (SED) fit of each system’s blended flux output was carried out, allowing for estimation of the bolometric flux from the primary and secondary components of each system. From the stellar M, L, and R values, the low-mass star relationships between L and M, and R and M, are compared against idealized expectations for such stars. An examination on the inclusion of these close M-dwarf/M-dwarf pairs in higher-order common proper motion (CPM) pairs is analyzed; each of the 5 systems has indications of being part of a CPM system. Unexpected distances on interesting objects found within the grid of parallactic reference stars are also presented, including a nearby M dwarf and a white dwarf.

Twenty Years of SpeX: Accuracy Limits of Spectral Slope Measurements in Asteroid Spectroscopy

Abstract We examined two decades of SpeX/NASA Infrared Telescope Facility observations from the Small Main-Belt Asteroid Spectroscopic Survey (SMASS) and the MIT–Hawaii Near-Earth Object Spectroscopic Survey (MITHNEOS) to investigate uncertainties and systematic errors in reflectance spectral slope measurements of asteroids. From 628 spectra of 11 solar analogs used for calibration of the asteroid spectra, we derived an uncertainty of on slope measurements over 0.8–2.4 μm. Air mass contributes to −0.92% μm−1 per 0.1 unit air mass difference between the asteroid and the solar analog and therefore for an overall 2.8% μm−1 slope variability in SMASS and MITHNEOS designed to operate within 1.0–1.3 air mass. No additional observing conditions (including the parallactic angle, seeing, and humidity) were found to contribute systematically to slope change. We discuss implications for asteroid taxonomic classification works. Uncertainties provided in this study should be accounted for in future compositional investigation of small bodies to distinguish intrinsic heterogeneities from possible instrumental effects.

A Possible Advantage of Telescopes with a Noncircular Pupil

Most telescope designs have a circular-shape aperture. We demonstrate that telescopes with an elongated pupil have better contrast, at lower separations, between a bright central star and a faint companion. We simulate images for an elongated-pupil telescope and for a circular-pupil telescope of equal aperture area and integration time, investigating specifically what is the maximal contrast for finding faint companions around bright stars as a function of angular separation. We show that this design gives better contrast at lower separation from a bright star. This is shown for diffraction-limited (for perfect and imperfect optics) and seeing-limited speckle images, assuming equal aperture area and observing time. We also show the results are robust to errors in measurement of the point spread function. To compensate for the wider point spread function of the short axis, images should be taken at different rotation angles, either by rotating the telescope around the optical axis or by allowing a stationary mirror array to scan different parallactic angles with time. Images taken at different rotation angles are added using the proper image coaddition algorithms developed by Zackay & Ofek. The final image has the same contrast in all angles, rather than in specific areas of diffraction nulls. We obtained speckle observations with a small, ground based elongated-aperture telescope and show the results are consistent with simulations.

Sub-band Image Reconstruction Using Differential Chromatic Refraction

Abstract Refraction by the atmosphere causes the positions of sources to depend on the airmass through which an observation was taken. This shift is dependent on the underlying spectral energy of the source and the filter or bandpass through which it is observed. Wavelength-dependent refraction within a single passband is often referred to as differential chromatic refraction (DCR). With a new generation of astronomical surveys undertaking repeated observations of the same part of the sky over a range of different airmasses and parallactic angles, DCR should be a detectable and measurable astrometric signal. In this paper we introduce a novel procedure that takes this astrometric signal and uses it to infer the underlying spectral energy distribution of a source; we solve for multiple latent images at specific wavelengths via a generalized deconvolution procedure built on robust statistics. We demonstrate the utility of such an approach for estimating a partially deconvolved image, at higher spectral resolution than the input images, for surveys such as the Large Synoptic Survey Telescope.

Characterizing the Performance of the NIRC2 Vortex Coronagraph at W. M. Keck Observatory

Abstract The NIRC2 vortex coronagraph is an instrument on Keck II designed to directly image exoplanets and circumstellar disks at mid-infrared bands L′ (3.4–4.1 μm) and M s (4.55–4.8 μm). We analyze imaging data and corresponding adaptive optics telemetry, observing conditions, and other metadata over a three-year time period to characterize the performance of the instrument and predict the detection limits of future observations. We systematically process images from 359 observations of 304 unique stars to subtract residual starlight (i.e., the coronagraphic point-spread function) of the target star using two methods: angular differential imaging (ADI) and reference star differential imaging (RDI). We find that for the typical parallactic angle (PA) rotation of our data set (∼10°), RDI provides gains over ADI for angular separations smaller than 0.″25. Furthermore, we find a power-law relation between the angular separation from the host star and the minimum PA rotation required for ADI to outperform RDI, with a power-law index of −1.18 ± 0.08. Finally, we use random forest models to estimate ADI and RDI post-processed detection limits a priori. These models, which we provide publicly on a website, explain 70%–80% of the variance in ADI detection limits and 30%–50% of the variance in RDI detection limits. Averaged over a range of angular separations, our models predict both ADI and RDI contrast to within a factor of 2. These results illuminate important factors in high-contrast imaging observations with the NIRC2 vortex coronagraph, help improve observing strategies, and inform future upgrades to the hardware.

Astroplan: An Open Source Observation Planning Package in Python

Abstract We present astroplan—an open source, open development, Astropy affiliated package for ground-based observation planning and scheduling in Python. astroplan is designed to provide efficient access to common observational quantities such as celestial rise, set, and meridian transit times and simple transformations from sky coordinates to altitude-azimuth coordinates without requiring a detailed understanding of astropy’s implementation of coordinate systems. astroplan provides convenience functions to generate common observational plots such as airmass and parallactic angle as a function of time, along with basic sky (finder) charts. Users can determine whether or not a target is observable given a variety of observing constraints, such as airmass limits, time ranges, Moon illumination/separation ranges, and more. A selection of observation schedulers are included that divide observing time among a list of targets, given observing constraints on those targets. Contributions to the source code from the community are welcome.

The Pointing Self-calibration Algorithm for Aperture Synthesis Radio Telescopes

Abstract This paper is concerned with algorithms for calibration of direction-dependent effects (DDE) in aperture synthesis radio telescopes (ASRT). After correction of direction-independent effects (DIE) using self-calibration, imaging performance can be limited by the imprecise knowledge of the forward gain of the elements in the array. In general, the forward gain pattern is directionally dependent and varies with time due to a number of reasons. Some factors, such as rotation of the primary beam with Parallactic Angle for Azimuth–Elevation mount antennas are known a priori. Some, such as antenna pointing errors and structural deformation/projection effects for aperture-array elements cannot be measured a priori. Thus, in addition to algorithms to correct for DD effects known a priori, algorithms to solve for DD gains are required for high dynamic range imaging. Here, we discuss a mathematical framework for antenna-based DDE calibration algorithms and show that this framework leads to computationally efficient optimal algorithms that scale well in a parallel computing environment. As an example of an antenna-based DD calibration algorithm, we demonstrate the Pointing SelfCal (PSC) algorithm to solve for the antenna pointing errors. Our analysis show that the sensitivity of modern ASRT is sufficient to solve for antenna pointing errors and other DD effects. We also discuss the use of the PSC algorithm in real-time calibration systems and extensions for antenna Shape SelfCal algorithm for real-time tracking and corrections for pointing offsets and changes in antenna shape.

Calibration Errors in Interferometric Radio Polarimetry

Abstract Residual calibration errors are difficult to predict in interferometric radio polarimetry because they depend on the observational calibration strategy employed, encompassing the Stokes vector of the calibrator and parallactic angle coverage. This work presents analytic derivations and simulations that enable examination of residual on-axis instrumental leakage and position-angle errors for a suite of calibration strategies. The focus is on arrays comprising alt-azimuth antennas with common feeds over which parallactic angle is approximately uniform. The results indicate that calibration schemes requiring parallactic angle coverage in the linear feed basis (e.g., the Atacama Large Millimeter/submillimeter Array) need only observe over 30°, beyond which no significant improvements in calibration accuracy are obtained. In the circular feed basis (e.g., the Very Large Array above 1 GHz), 30° is also appropriate when the Stokes vector of the leakage calibrator is known a priori, but this rises to 90° when the Stokes vector is unknown. These findings illustrate and quantify concepts that were previously obscure rules of thumb.

Direction-dependent Corrections in Polarimetric Radio Imaging. I. Characterizing the Effects of the Primary Beam on Full-Stokes Imaging

Abstract Next generation radio telescope arrays are being designed and commissioned to accurately measure polarized intensity and rotation measures (RMs) across the entire sky through deep, wide-field radio interferometric surveys. Radio interferometer dish antenna arrays are affected by direction-dependent (DD) gains due to both instrumental and atmospheric effects. In this paper, we demonstrate the effect of DD errors of the parabolic dish antenna array on the measured polarized intensities of radio sources in interferometric images. We characterize the extent of polarimetric image degradation due to the DD gains through wide-band VLA simulations of representative point-source simulations of the radio sky at L band (1–2 GHz). We show that at the 0.5 gain level of the primary beam there is significant flux leakage from Stokes I to Q, U amounting to 10% of the total intensity. We further demonstrate that while the instrumental response averages down for observations over large parallactic angle intervals, full-polarization DD correction is required to remove the effects of DD leakage. We also explore the effect of the DD beam on the RM signals and show that while the instrumental effect is primarily centered around 0 rad-m−2, the effect is significant over a broad range of RM requiring full polarization DD correction to accurately reconstruct the RM synthesis signal.

Change in the Fusion Limit by Insertion of a Middle Image Equally Dividing the Parallactic Angle of 3D Stereoscopic Images.

The purpose of this study was to identify and clarify the requirements for 3D stereoscopic images that do not cause viewing discomfort to the human eye even when the protrusion distance is large. A total of 140 healthy men and women aged 14 to 79 years participated in this study. We first measured the fusion limits in these participants using two 3D stereoscopic images. We then measured the expansion of the fusion limit by inserting a middle image in a region located equally parallax from the two images. The results showed that the fusion limits were significantly expanded (p<0.01) after inserting the middle image. Insertion of middle images with parallax can extend the fusion limit. This method was shown to be an effective for viewing 3D stereoscopic images without causing discomfort.

The 492 GHz emission of Sgr A* constrained by ALMA

We report linearly polarized continuum emission properties of Sgr A* at $\sim$492 GHz, based on the Atacama Large Millimeter Array (ALMA) observations. We used the observations of the likely unpolarized continuum emission of Titan, and the observations of C\textsc{i} line emission, to gauge the degree of spurious polarization. The Stokes I flux of 3.6$\pm$0.72 Jy during our run is consistent with extrapolations from the previous, lower frequency observations. We found that the continuum emission of Sgr A* at $\sim$492 GHz shows large amplitude differences between the XX and the YY correlations. The observed intensity ratio between the XX and YY correlations as a function of parallactic angle may be explained by a constant polarization position angle of $\sim$158$^{\circ}$$\pm$3$^{\circ}$. The fitted polarization percentage of Sgr A* during our observational period is 14\%$\pm$1.2\%. The calibrator quasar J1744-3116 we observed at the same night can be fitted to Stokes I = 252 mJy, with 7.9\%$\pm$0.9\% polarization in position angle P.A. = 4.1$^{\circ}$$\pm$4.2$^{\circ}$. The observed polarization percentage and polarization position angle in the present work appear consistent with those expected from longer wavelength observations in the period of 1999-2005. In particular, the polarization position angle at 492 GHz, expected from the previously fitted 167$^{\circ}$$\pm$7$^{\circ}$ intrinsic polarization position angle and (-5.6$\pm$0.7)$\times$10$^{5}$ rotation measure, is 155$^{+9}_{-8}$, which is consistent with our new measurement of polarization position angle within 1$\sigma$. The polarization percentage and the polarization position angle may be varying over the period of our ALMA 12m Array observations, which demands further investigation with future polarization observations.

Dual differential polarimetry. A technique to recover polarimetric information from dual-polarization observations

Current mm/submm interferometers, like the Atacama Large mm/submm Array (ALMA), use receivers that register the sky signal in a linear polarization basis. In the case of observations performed in full-polarization mode (where the cross-correlations are computed among all the polarization channels) it is possible to reconstruct the full-polarization brightness distribution of the observed sources, as long as a proper calibration of delay offsets and leakage among polarization channels can be performed. Observations of calibrators, preferably with some linear polarization, with a good parallactic angle coverage are usually needed for such a calibration. In principle, dual-polarization observations only allow us to recover the Stokes $I$ intensity distribution of the sources, regardless of the parallactic angle coverage of the observations. In this paper, we present a novel technique of dual differential polarimetry that makes it possible to obtain information related to the full-polarization brightness distribution of the observed sources from dual-polarization observations. This technique is inspired in the Earth-rotation polarization synthesis and can be applied even to sources with complex structures.

Revisiting the impact of atmospheric dispersion and differential refraction on widefield multiobject spectroscopic observations

(Abridged) Atmospheric dispersion and field differential refraction impose severe constraints on widefield MOS observations. Flux reduction and spectral distortions must be minimised by a careful planning of the observations -- which is especially true for instruments that use slits instead of fibres. This is the case of VIMOS at the VLT, where MOS observations have been restricted, since the start of operations, to a narrow two-hour range from the meridian to minimise slit losses. We revisit in detail the impact of atmospheric effects on the quality of VIMOS-MOS spectra. We model slit losses across the entire VIMOS FOV as a function of target declination. We explore two different slit orientations at the meridian: along the parallactic angle (North-South), and perpendicular to it (East-West). We show that, for fields culminating at zenith distances larger than 20 deg, slit losses are minimised with slits oriented along the parallactic angle at the meridian. The two-hour angle rule holds for these observations using N-S orientations. Conversely, for fields with zenith angles smaller than 20 deg at culmination, losses are minimised with slits oriented perpendicular to the parallactic angle at the meridian. MOS observations can be effectively extended to plus/minus three hours from the meridian in these cases. In general, night-long observations of a single field will benefit from using the E-W orientation. All-sky or service mode observations, however, require a more elaborate planning that depends on the target declination, and the hour angle of the observations. We establish general rules for the alignment of slits in MOS observations that will increase target observability, enhance the efficiency of operations, and speed up the completion of programmes -- a particularly relevant aspect for the forthcoming spectroscopic public surveys with VIMOS.

The kinematical evolution of the Galactic disk

We present preliminary results from follow-up observations of a carefully selected sample of subgiant stars from RAVE and Geneva-Copenhagen surveys. We find evidence of rapid saturation of the heating mechanism in the disk, with an abrupt increase of the velocity dispersion for stars older than 9 Gyr. 1. SAMPLE DEFINITION AND FOLLOW-UP OBSERVATIONS Using high resolution spectroscopy data (7) showed the value of subgiants for dating the Galactic disk. We have selected ∼2000 subgiants candidates from the RAVE survey using RAVEs stellar parameters (6, 8). We have also selected 404 subgiants (no binaries) from the Geneva-Copenhagen survey (GCS) (3 )i n the Mv−Teff plane. We performed follow-up observations with the Double Beam Spectrograph (DBS) instrument mounted at the ANU 2.3 m telescope in Siding Spring Observatory. We use a long slit of 5 �� width and the 300B grating, giving a spectral resolution of R = /∼400. The recorded spectra cover the wavelength range from 3200 A to 6600 A. Observations consist of a sequence of target exposure, standard stars, calibration lamps, flats and bias. During the observational campaign we used a wide slit of 5 �� , which assures that 100% of the star light is collected (depending on the seeing), while avoid tracking problems. We also placed the slit parallel to the direction of atmosphere dispersion, i.e, aligning the slit at the parallactic angle to avoid recording incorrect intensities as a function of wavelength that could spoil our flux calibration. Standard stars with the same instrumental setup were obtained each night covering a large range of airmass over the night. This allows us to control the atmospheric extinction in the observed spectra. The final spectra present a typical S/N∼130 at 5500A and a S/N∼80 for the Ca II H & K region around 3950 A. A total of 1253 subgiant candidates spectra were obtained. 2. STELLAR PARAMETERS FROM SPECTROPHOTOMETRY We derived the stellar parameters using a chi-square minimization technique using empirical model atmospheres from the MILES library (4). The library consist of ∼1000 stars spanning a large range in atmospheric parameters. The spectra cover the range 3525-7500A at 2.3A (FWHM) spectral resolution. This technique allows us to derive accurate parameters from low resolution spectrophotometry via flux calibrated spectra. For reddening corrections we use the standard value of R(V) = A(V)/ E(B − V) = 3.1. We redden the model and we use the E(B − V) as a free parameter together with Teff , (M/H) and log g in the 2 fitting. Reddening effects are not large for our stars, as the selected RAVE stars are at |b |≥ 25 degrees and the GCS stars are in a very local volume with a radius lower than 100 pc.

Analysis of Image Rotation for Aerial Remote Sensor with Off-Axis three-Reflective Optical System

In order to improve the dynamic state resolution of aerial remote sensor, it is indispensable to analyzing image rotation of aerial remote sensor. According to optical reflection vector theory, study on imaging character of aerial remote sensor with off-axis three-reflective optical system. At first, a simple mathematics model is abstracted from the aerial remote sensor. In the Cartesian coordinate system, compute the image plane revolution vector quantity caused by scan mirror rotating of parallactic angle and depression angle by analysis of image rotation direction for aerial remote sensor with off-axis three-reflective optical system applying coordinate conversion and geometrical optics, provide a theoretical resource for the application of the drift mechanism (eliminating image rotation mechanism). Using this method can calculate exactly image motion and image motion compensation error of image planeand image motion quantity less than 0.003mm. In conclusion, the result of the computation improves Modulation Transfer Function (MTF) of optical system.

The Comfortable Parallactic Angle of Stereoscopic for Depth Presentation Position on Two Different Celestial Bodies

The Comfortable Parallactic Angle of Stereoscopic for Depth Presentation Position on Two Different Celestial Bodies