Atmospheric Modulation Transfer Function Research Articles

Design of Photoelectric Detection System Used for Atmospheric Microdroplets and Modulation Transfer Function Model of Gaussian Beam

Atmospheric corrosion is an electrochemical corrosion process of metal materials in the atmospheric environment. Microdroplet phenomenon is an experimental phenomenon in the early stage of atmospheric corrosion, which is closely related to atmospheric corrosion. Photoelectric detection of microdroplet phenomenon has become a technical means to study atmospheric corrosion. A set of microdroplet photoelectric detection systems with small size, high integration, and low detection limit is designed and constructed. First, the microdroplet optical chip is designed and fabricated. The microdroplet chip with a single function is replaced by the microdroplet chip with optical microlenses, and the miRNA is detected on the photoelectric platform of the optical chip. The optical fiber is adopted to replace the traditional objective lens to excite the optical path, reduce the volume of the spatial optical path, and realize the miniaturization of the photoelectric detection system. Based on this system, the nonlinear relationship between atmospheric turbulence effect and atmospheric optical parameters is analyzed with Gaussian beams propagating in the atmosphere. In the experiment, the detection range of the photoelectric detection system is 5 nM~100 nM, and the linear correlation is 0.9958. The signals of Cy3 and Cy5 are detected by two groups of photomultiplier tube (PMT) to realize the detection of miRNA. Microlenses enhance the intensity of the photoelectric signal and reduce the detection limit. Microdroplets are used to encapsulate miRNA, reduce the amount of detection material, and solve the degradation of detection material by RNase. The modulation transfer function model of Gaussian beam is established with the assistance of the photoelectric detection system, which is suitable for the case that cannot be ignored in Kolmogorov turbulence under the action of internal/external scale.

Wave structure function and long-exposure MTF for laser beam propagation through non-Kolmogorov turbulence

Abstract The degrading effects of atmospheric turbulence on an imaging system can be characterized by the atmospheric modulation transfer function (MTF). In this paper, we derived analytically a new expression for the wave structure function (WSF) of a Gaussian-beam based on the weak fluctuation theory. We assumed the beam-wave is propagating through a horizontal path experiencing isotropic and homogeneous non-Kolmogorov atmospheric turbulence where the power spectrum has a generalized spectral power-law exponent which varies between 3 and 4 instead of the fixed classical Kolmogorov power-law exponent of 11/3. Using the WSF, we derived mathematical expressions for the spatial coherence radius and the long-exposure turbulence MTF of the Gaussian-beam wave. These new expressions were used to analyze the influence of power-law variations and beam sizes on the WSF and quality of imaging systems. The simulation results show that different exponent values produce varying effects on both WSF and imaging systems.

Influence of moderate-to-strong non-Kolmogorov turbulence on the imaging system by atmospheric turbulence MTF

The atmospheric turbulence modulation transfer function (MTF) which describes the degrading effect of atmospheric turbulence on imaging system is investigated theoretically for plane and spherical waves propagating through moderate-to-strong non-Kolmogorov turbulence. In the investigation, the effective non-Kolmogorov spectral model is adopted, and it modifies the conventional non-Kolmogorov spectral model with a modified frequency filter function. The new expressions cover a more wide range of non-Kolmogorov turbulence strength, and reduce correctly to previously published analytic expressions for both weak non-Kolmogorov turbulence and moderate-to-strong (or strong) Kolmogorov turbulence cases. Numerical calculations show that the MTF model derived in this work deviates from those obtained with the Rytov theory as turbulence strength increases up to moderate-to-strong (or strong) non-Kolmogorov turbulence regime.

Errata: Reanalysis of turbulence effects on short-exposure passive imaging

he standard method for modeling the atmospheric short-exposure modulation transfer function (MTF) is due to Fried. This method involves evaluating the impact of amplitude and phase modulations of the propagating wavefront after the removal of the mean wavefront tilt. This tilt is determined by a least-squares analysis. We retain a term involving the correlation between tilt-corrected phase and computed tilt vector that was formerly assumed to be zero. Inclusion of this term yields a new turbulence-strength-dependent effect that degrades performance at high integrated turbulence levels and also predicts super-resolution effects at lower integrated turbulence levels. An analytical approximation is derived from this analysis that describes the new MTF model as a function of three dimensionless parameters related to the angular frequency, system aperture diameter, and integrated turbulence strength.

Removing atmospheric MTF and establishing an MTF compensation filter for the HJ-1A CCD camera

The total image modulation transfer function (MTF) comprises imaging system MTF and atmospheric MTF, both of which can produce blurring effects in remote-sensing images. Imaging system MTF, one of the important specifications of the imaging system, is used to characterize the radiometric response of the sensor. Atmospheric MTF, which consists of aerosol MTF and turbulence MTF, usually changes with external atmospheric conditions. To obtain the MTF of the imaging system, the atmospheric MTF has to be removed from the total image MTF. This study aims to determine a method for removing the atmospheric MTF for the charge-coupled device (CCD) camera on-board the Huanjing 1A satellite (HJ-1A). The aerosol MTF and the turbulence MTF in the CCD images were first predicted based on the aerosol optical depth (AOD) derived by dark target and reanalysis of data from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR). Then, the MTFs of the CCD camera were retrieved by removing the aerosol and turbulence MTFs from the total on-orbit image MTFs that were calculated from the linear features on CCD images. For the HJ-1A CCD camera, results show that the MTF values at Nyquist frequency increased by about 10% after the atmospheric MTFs were removed. The total image MTF became degraded by about 50% when AOD was high or turbulence was strong. Furthermore, this study has established an MTF compensation (MTFC) filter for the HJ-1A by modifying the ‘modified inverse filter (MIF)’ approach. Results illustrate that the effective instantaneous field of view (EIFOV) of the restored image improved from 78 to 41 m, while the noise level of the model was well controlled. This research demonstrates that the modified approach is effective for sensors with low MTF values.

Atmospheric scattering and turbulence modulation transfer function for CCD cameras on CBERS-02b and HJ-1A/1B

Atmospheric turbulence and aerosol scattering can produce the blurring of the remotely sensed image. The degrading effect is usually quantified by atmospheric modulation transfer function (MTF). However, this effect behaves differently with different remote sensors. The effort of this article is to study the different degrading effects of aerosol MTF and turbulence MTF between charge-coupled device (CCD) camera on China–Brazil Earth Resources Satellite-02b (CBERS-02b) and on Huan Jing-1A/1B satellite (HJ-1A/1B). Specifically, a corrected aerosol MTF model is established based on classical solution of small-angle approximation (SAA) model by considering the MTF and the effective instantaneous field of view (EIFOV) of CCD cameras. By assuming many different atmospheric conditions, the aerosol MTF and turbulence MTF for two CCD cameras are evaluated. It is found that the output aerosol MTF of CCD camera on HJ-1A/1B causes more degrading effect than that of CBERS-02b under the same atmospheric condition. However, the situation reverses for the turbulence MTF. Furthermore, CCD images acquired over Beijing, China, by CBERS-02b and HJ-1A/1B on four different dates are selected. The overall atmospheric MTF for these images are determined based on the aerosol products from Aerosol Robotic Network (Aeronet) and radiosounding data. Results indicate that the overall atmospheric MTF of CBERS-02b CCD camera reduces image quality more seriously than that of HJ-1A/1B CCD camera. Additionally, the atmospheric MTF compensation is performed and evaluated for these CCD images based on the overall atmospheric MTF.

Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence

A generalized exponential spectrum model is derived, which considers finite turbulence inner and outer scales and has a general spectral power law value between the range 3 to 5 instead of standard power law value 11/3. Based on this generalized spectrum model, a new generalized long exposure turbulence modulation transfer function (MTF) is obtained for optical plane and spherical wave propagating through horizontal path in weak fluctuation turbulence. When the inner scale and outer scale are set to zero and infinite, respectively, the new generalized MTF is reduced to the classical generalized MTF derived from the non-Kolmogorov spectrum.

Atmospheric modulation transfer function in the infrared.

In high-resolution ultranarrow field-of-view thermal imagers, image quality over relatively long path lengths is typically limited by atmospheric degradation, especially atmospheric blur. We report our results and analyses of infrared images from two sites, Fort A. P. Hill and Aberdeen Proving Ground. The images are influenced by the various atmospheric phenomena: scattering, absorption, and turbulence. A series of experiments with high-resolution equipment in both the 3-5- and 8-13-microm regions at the two locations indicate that, as in the visible, image quality is limited much more by atmosphere than by the instrumentation for ranges even of the order of only a few kilometers. For paths close to the ground, turbulence is more dominant, whereas for paths involving higher average elevation, aerosol modulation transfer function (MTF) is dominant. As wavelength increases, turbulence MTF also increases, thus permitting aerosol MTF to become more dominant. A critical role in aerosol MTF in the thermal infrared is attributed to absorption, which noticeably decreases atmospheric transmission much more than in the visible, thereby reducing high-spatial-frequency aerosol MTF. These measurements indicate that atmospheric MTF should be a basic component in imaging system design and analysis even in the infrared, especially as higher-resolution hardware becomes available.

Criteria for satellite image restoration success

Many properties of the atmosphere affect the quality of images propagating through it by blurring and reducing their contrast. The atmospheric path involves several limitations, such as scattering, absorption of light, and turbulence, which degrade the image. Recently developed atmospheric filters, which correct for turbulence blur, aerosol blur, and path radiance simultaneously, are implemented here in the digital restoration of Landsat thematic mapper (TM) imagery. The turbulence modulation transfer function (MTF) is calculated from meteorological data or estimated if no meteorological data were measured. Aerosol MTF is consistent with optical depth. The product of the two yields atmospheric MTF, which is implemented in the atmospheric filter. Restoration improves smallness of size of both resolvable detail and contrast. Restorations are quite apparent even under clear weather conditions. A way to evaluate restoration improvement is presented here by the use of quantitative criteria as well as subjective opinions of human observers in perception experiments. Not all the restoration criteria represent improvement in the same tested image under the same restoration conditions. When one criterion suggests an enhancement, there is a chance that another one might represent a lower value for restoration success.

Restoration of atmospherically blurred images according to weather-predicted atmospheric modulation transfer functions

Restoration for actual atmospherically blurred images is per- formed using an atmospheric Wiener filter that corrects simultaneously for both turbulence and aerosol blur by enhancing the image spectrum primarily at those high frequencies least affected by the jitter or random- ness in a turbulence modulation transfer function (MTF). The correction is based on weather-predicted rather than measured atmospheric MTFs. Both turbulence and aerosol MTFs are predicted using meteorological parameters measured with standard weather stations at the time and location where the image was recorded. A variety of weather conditions and seasons are considered. Past results have shown good correlation between measured and predicted atmospheric MTFs. Here, the pre- dicted MTFs are implemented in actual image restoration and quantita- tive analysis of the MTF improvement is presented. Corrections are shown also for turbulence blur alone, for aerosol blur alone, and for both together. © 1997 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(97)01511-0)

Effect of the inner scale of turbulence on the atmospheric modulation transfer function

The effect of the inner scale of turbulence on the atmospheric modulation transfer function (MTF) is analyzed. It is shown that owing to this effect the turbulence MTF has all the main features of the overall measured atmospheric MTF, including different behaviors in the low- and high-frequency ranges, a knee, and dependence on the wavelength. It is also shown that the mismatches between the overall measured atmospheric MTF and the predicted turbulence MTF might be eliminated by use of a theoretical model with a finite inner scale of turbulence for the turbulence MTF and an accurate interpretation of the optical measurements of the refractive-index structure characteristic. Therefore no revision of the classical aerosol MTF theory is required to interpret the measured data.

Prediction of overall atmospheric modulation transfer function with standard weather parameters: comparison with measurements with two imaging systems

The overall atmospheric modulation transfer function (MTF) is essentially the product of the turbulence and aerosol MTFs. Models describing meteorological dependences of both <i>C</i>²<i>n</i> (where <i>Cn</i> is the refractive index structure coefficient) and the coarse aerosol size distribution have been developed previously. Here, they are used to predict the turbulence MTF, aerosol MTF, and overall atmospheric MTF according to the weather. Comparison of predictions with measurements yields very low mean squared normalized error and suggests that such prediction models can also be very useful in image restoration based on weather data at the time and general location in which the image was recorded. An interesting aspect of this work is that measurements of the aerosol MTF with different imaging instrumentation are very different, as expected from theory developed previously concerning the practical aerosol MTF actually recorded in the image. This is dependent on instrumentation parameters. This experimental verification with two different imaging systems supports the model that the "practical" aerosol MTF is very dependent on instrumentation.

Target acquisition modeling for contrast-limited imaging: effects of atmospheric blur and image restoration

The incorporation of atmospheric aerosol and turbulence effects into visible, near-infrared, and thermalinfrared target acquisition modeling is considered. We show how the target acquisition probabilities and, conversely, the ranges at which objects can be detected are changed by the inclusion of atmospheric effects. It is assumed that images are contrast limited rather than noise limited, as is indeed the case with most visible, near-infrared, and thermal infrared sensors. For short focal lengths with low angular magnification, atmospheric effects on target acquisition are negligible. However, for longer focal lengths with large angular magnification, resolution is limited by the atmosphere, and this has a strong adverse effect on target acquisition probabilities, times, and ranges. The considerable improvement possible with image correction for atmospheric blur automatically in a fraction of a second is significant for contrast-limited imaging and is also discussed. Knowledge of the atmospheric modulation transfer function is essential to good system design and is also useful in image restoration for any type of target or object. Finally, a new target-transferfunction model is suggested that considers the overall image-spectrum target received by the human visual system rather than only the main harmonic detail as in the Johnson chart model. [ J. Johnson , in Proceedings of Seminar on Direct-Viewing Electro-Optical Aids to Night Vision ( IDA, Alexandria, Va., 1966), p. 177.]

Modal compensation of atmospheric turbulence with the use of Zernike polynomials and Karhunen–Loève functions

Atmospheric Karhunen–Loeve functions are the optimal set of basis functions for modal atmospheric compensation. They are seldom applied in practice on account of their nonanalytical nature. A pseudoanalytical set of these functions is constructed with a least-squares-fitting procedure. To produce an analytical expression for the optical resolution of modal atmospheric compensation, a modified form of structure functions is used and applied to the compensated wave front. This results in analytical residual phase structure functions for Zernike polynomials and pseudoanalytical residual phase structure functions for Karhunen–Loeve functions. With these structure functions it is found that the modulation transfer function (MTF) after modal compensation is the product of the telescope MTF and the uncompensated atmospheric MTF under the assumption of isotropic compensating phase. Comparison with an accurate numerical method shows that the approximated analytical method developed is much faster and gives reasonably accurate results, especially for high-order compensations.

High-resolution restoration of images distorted by the atmosphere, based on an average atmospheric modulation transfer function

A new method of real-time high-resolution imaging through the atmosphere is presented. This technique is based on knowledge of average atmospheric modulation transfer function (MTF) at the time the image is received. Atmospheric effects are modeled by a noisy spatial frequency filter including an average component described by the average atmospheric MTF and a noisy component modeled by the atmospheric point spread function's power spectral density. The noisy component represents random changes in the atmospheric MTF. Analytical results are accompanied by experimental image restoration examples, indicating significant image quality improvement based on knowledge of average atmospheric MTF, which includes both turbulence and aerosol MTF components. This method can be used to help overcome the jitter characteristics of turbulence, and is capable of yielding real-time image restoration with resolution limited essentially only by the hardware itself. Turbulence blur, aerosol blur, and contrast degradation are all corrected simultaneously, unlike adaptive optics, which corrects for turbulence only.

Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere

Although turbulence is usually considered to be the primary cause of image blur, simultaneous and independent measurements of overall atmospheric modulation transfer function (MTF) and turbulence MTF over fairly long horizontal paths at 15-m average elevation indicate that, even at midday, aerosol MTF deriving from forward scatter is usually more dominant than turbulence MTF. Three different experimental techniques are used, two passive and one active. Aerosol MTF measurements are accompanied by actual meteorological and coarse aerosol size distributions and scattering parameters at the times of MTF measurements. The wavelength dependence of aerosol and therefore of overall atmospheric MTF can be significant. This wavelength dependence and a usually well-defined knee can in no way be due to turbulence but can be explained by a significant aerosol MTF deriving from typical aerosol size distributions representative of other climates as well. Measurements confirm that the narrower the open-atmosphere aerosol scattering patterns and the greater the scattering densities, the greater the degradations of aerosol MTF and, consequently, of overall atmospheric MTF. Results imply that system design and image-restoration algorithms based on atmospheric turbulence only may often lead to image quality that is much poorer than if aerosol MTF is considered, too, with its proper proportional effect on imaging through the atmosphere. Whereas adaptive optics cannot correct for aerosol-derived blur, digital image restoration can.

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function: reply to comment

New exact numerical calculations as well as exact calculations in J. Opt. Soc. Am. A10, 172 ( 1993) indicate that the approximations in the Comment in J. Opt. Soc. Am. A11, 1175 ( 1994) are based on faulty perceptions of basic scattering phenomena and on a misreading of our paper. The Comment does not sufficiently consider effects of instrumentation. Whereas our model refers to the aerosol modulation transfer function (MTF) in the image plane, the values of maximum angles for scattered (θS) and unscattered (θ0) light used in the Comment refer to the optics plane. The Comment does not consider the fact that dynamic range limits (θS) in the image, whereas limited spatial-frequency bandwidth broadens θ0 in the image, each by orders of magnitude. Therefore the Comment’s conclusion contradicts experimental results obtained by numerous researchers. The Comment’s conclusion that aerosol MTF is insignificant is based on that author’s own experiments, in which clear weather and haze atmospheric MTF (composed of turbulence and aerosol MTF’s) could not be measured, the reason being insufficient equipment resolution, rather than insignificant turbulence or aerosol MTF. Furthermore, the claim in our original paper that aerosol MTF is extremely significant has since been supported by many different types of experiments that included short and long exposures, thermal imaging, and image restoration based on atmospheric MTF, including a highly significant practical, uniquely shaped, aerosol MTF.

Restoration of thermal images distorted by the atmosphere, using predicted atmospheric modulation transfer function

Restoration of thermal images distorted by the atmosphere, detected with a focal plane array (FPA) Pt-Si thermal imaging system, is presented. The restoration method is based upon atmospheric modulation transfer function (MTF) analysis. Using turbulence and aerosol MTF prediction models, atmospheric distortions and image degradation are modeled. Restoration results indicate significant improvement in image quality. However, it is critical to include the unique shape of aerosol MTF when modeling atmospheric MTF in order to obtain good restoration.

Incorporation of atmospheric blurring effects in target acquisition modeling of thermal images

Recent investigation of atmospheric modulation transfer function (MTF) in the thermal IR has shown significant spatial frequency dependence. This dependence is related to aerosol forward scatter as well as particulate absorption effects, shown to be primary contributors to blur in thermal imaging through the atmosphere. One of the primary models for target acquisition is the Institute for Defence Analysis variant of the Night Vision Laboratory (IDA/NVL) target acquisition model; in this paper, this model is revised to include atmospheric MTF spatial frequency dependence. It is shown how the target acquisition probabilities and, conversely, the range at which targets can be detected are changed by the inclusion of atmospheric effects. Under weak turbulence conditions target acquisition probabilities are better than predicted by the IDA/NVL model at shorter ranges. For very strong turbulence, as at midday on hot days, target acquisition probabilities decrease. Effects of real-time image restoration are discussed.

Effects of practical aerosol forward scatter of infrared and visible light on atmospheric coherence diameter

A correction to the definition of the atmospheric coherence diameter is suggested here, based on the existence of a practical instrumentation-based aerosol modulation transfer function (MTF), which is often the dominant ingredient of the atmospheric MTF. As defined classically by Fried about 25 yr ago, atmospheric MTF and coherence diameter were related to turbulence MTF only. Lutomirski considered diftractive aerosols, too, but did not consider effects of instrumentation on scattering angles actually recorded in the image. These are limited in the real world by instrumentation to milliradians, rather than by the broad angular spread of diffraction to radians. In the case of a Gaussian approximation of the practical aerosol MTF, an analytical expression is derived for the practical aerosol-derived coherence diameter. This parameter is related to the practical aerosol MTF's cutoff frequency, and to its asymptotic value at high spatial frequencies. Thus, a more general concept of atmospheric coherence diameter is proposed here, which is relevant to actual real-world imaging systems, whether they are passive or active. Quantitative validation of the theory is presented, based on both simulations and actually measured atmospheric MTFs in both the visible and thermal infrared spectral ranges. Overall atmospheric coherence diameter is determined generally by the smaller of the turbulence and practical aerosol coherence diameters, depending on optical depth. The results here appear applicable particularly to cost-effective thermal imaging system design, although applications are considered, too, for the visible and near infrared. For example, blur deriving from aerosol scatter should have much less effect in coherent detection laser radar (LIDAR) than in direct detection imaging.