RU2628991C1 - Method of determination of surface albedo - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: method involves measurement of the total radiation Q in the area of the examined surface with an actinometric device, determination of the brightness L of the examined surface and calculation of the albedo value A of the examined surface according to the mathematical dependence: A =αL+βQ+γ, where α, β, γ are coefficients of the regression equation.

EFFECT: providing the possibility of remote automated data collection, reducing labor and measurement time.

8 cl, 5 dwg

Description

The invention relates to measuring, photo and video equipment, hydrometeorological equipment and methods for monitoring the parameters of radiant heat transfer on the studied surfaces, and can be used to determine the albedo of the surface.

The thermal balance of the surface is one of the key components of many models describing atmospheric and oceanic circulation, ice growth and melting processes, forecasts of permafrost “behavior”, which makes its accurate calculation extremely important for obtaining representative and relevant information “at the output” of the simulation. In turn, the thermal balance of the surface depends on the albedo - the characteristics of the reflectivity of the surface.

Today, despite the high importance of the albedo characteristics in calculating the energy balance of surfaces and modeling hydrometeorological parameters, in situ measurements of albedos are carried out using time-consuming and time-consuming direct instrumental measurements at specific points, for example, using pyranometers. They are deprived of the possibility of on-line spot measurements over large areas. This imposes great restrictions on the volume of accumulated data on the albedo characteristic, the accuracy of the input parameters of models taking this parameter into account, and, as a result, the results of the simulation itself. Satellite observations, in turn, have lower accuracy and a large spatial scale of measurements, strongly depend on the coincidence of meteorological conditions in the observation area with the time of passage of the satellite capable of performing these measurements over the measurement area.

The prior art method for determining albedo, including actinometric observations with the measurement of the total radiation incident on a reflecting surface of the reflecting surface, determining the albedo by the ratio of reflected radiation to incident, the studied limited fragment is fixed before measurements and a device is used concentrically to stabilize the reflection, then produce reflection stabilization measuring the total incident radiation or its components, direct and scattered radiation, as well as reflected radiation, at this, as part of the reflected radiation, measure the joint fluxes of radiation reflected from the studied fragment from the stabilized background ring lining, as well as the disorganized background behind the contour of the ring background lining, process the measurement results and determine the albedo value A _ism ^I according to a certain formula:

,

,

. (см. Патент RU 2145074, опубликован 27.01.2000).then close the test fragment with a round liner from the background albedo, make repeated measurements of at least the reflected radiation, and after processing the measurement results, determine the second albedo value A _IS ^II taking into account the combined effect of the flows, then find the difference of the measured A _IS ^I and A _IS ^II taking into account the angular characteristics of their influence on the readings of the device and determine the true value of the albedo of the studied fragment by the formula

. (see Patent RU 2145074, published January 27, 2000).

The disadvantage of this method is the difficulty in determining the albedo, the need to use complex and / or expensive equipment, high inertia and, as a consequence, the inability to quickly and efficiently collect data on large areas of the studied surfaces, the lack of remote application and automation of data collection.

The objective of the invention is to provide a method for simple and quick data collection on the surfaces under study using available technical means for the rapid determination of their albedo.

The objective of the invention is solved by the method for determining the albedo of surfaces, which consists in the fact that using an actinometric device measure the total radiation Q in the area of the test surface, determine the brightness L of the test surface and determine the albedo A of the test surface by mathematical dependence:

A = αL + βQ + γ, where

α, β, γ are the coefficients of the regression equation.

The coefficients of the regression equation α, β, γ can be determined by calculation based on the results of determining the brightness of the reference surface with a known albedo and measuring the total radiation in the area of the reference surface.

The brightness of the reference surface can be determined using a device for measuring brightness or using a photo-recording device.

In addition, the coefficients of the regression equation α, β, γ can be determined by mathematical modeling.

The brightness L of the test surface can be determined using a device for measuring brightness.

In addition, the brightness L of the test surface can be determined by shooting it using a photo-recording device, while the brightness value L is determined by the mathematical dependence:

L = L'K _exp , where

K _exp is the normalization coefficient equal to l _n / l ₁₂₈ > where l _n is the brightness of the image in the RGB space, l ₁₂₈ is the average brightness of the image in the RGB space, equal to 128;

L 'is the brightness of the image of the investigated surface, equal to GN ² / qtS, where G is the coefficient of the exposure index technique;

N is the aperture number of the photo-recording device;

q is the coefficient characterizing the parameters of the lens of the photo-recording device;

t is the shutter speed of the photo-recording device, s;

S is the equivalent photosensitivity of the photo recorder, ISO units.

The surveyed surface is surveyed and the total radiation Q in its zone is measured, mainly observing the horizontalness and mutual parallelism of the investigated surface, the planes of the sensing element of the actinometric device and the photosensitive element of the photo-recording device.

Surveyed surface survey and measurement of total radiation Q are carried out mainly simultaneously.

The technical result of the invention is to reduce the complexity of determining the albedo of surfaces, reduce the time required to collect data on the surfaces to be studied by reducing the number of necessary operations, and also due to the possibility of remote and automated data collection on the surfaces to be studied using simple and affordable equipment.

The invention is illustrated using the drawings, where in FIG. 1 shows the use of a technical solution using the example of a camera and a pyranometer for collecting data on the surface under study; in FIG. Figure 2 shows an example of the state of the ice surface of Lake Onega during measurements (EGF 31.21 mm, shooting distance ~ 1.5 m); in FIG. Figure 3 shows a graph of the variability of the observed and calculated albedos at different points of the polygon; in FIG. 4 shows a graph of linear albedo regression and normalized brightness of the subject (test surface) according to the experiment; in FIG. Figure 5 shows a graph of the variability of the albedo observed and the albedo calculated by different methods according to images at different points of the experimental test site.

The method for determining the albedo of a surface according to the proposed invention is that to determine the albedo A of the test surface, the total radiation Q in the area of the test surface is determined, and the brightness L of the test surface is also determined. After determining the parameters Q and L (total radiation and brightness of the test surface), determine the value of the albedo A of the test surface by mathematical dependence:

,

,

where α, β, γ are the coefficients of the regression equation, determined either by the method of mathematical modeling or empirically, i.e. obtained by calculation based on the results of determining the brightness of the reference surface with a known albedo and measuring the total radiation in the area of the reference surface.

The total radiation Q in the area of the investigated surface, as well as in the area of the reference surface, is measured using an actinometric device, for example, an M80-m pyranometer (or any other actinometric device).

The brightness L of the test surface, as well as the brightness of the reference surface can be determined using any device for measuring brightness, for example, a brightness meter.

Also, the brightness L of the test surface and the reference surface can be determined by shooting it using a photo-recording device (camera 1, or a camera built into any technical device, for example, a mobile phone, smartphone, tablet, etc.).

In recent years, technological progress has developed very much at the level of household appliances. A large number and types of cameras have appeared, which are built into a huge number of household electrical portable devices, and are divided into a large number of varieties: SLR, mirrorless, compact, light field cameras, etc. Digital photography has also evolved in the wake of this progress. The precision of cameras as equipment has increased even at the level of consumer technology, new international exposure metering standards have emerged that correspond to the realities of our time. All this allows us to consider the camera as a measuring device with a rich application potential.

Modern cameras, regardless of the complexity of their design and the technology used, contain the key elements: lens, shutter, photosensitive surface (matrix); and obey all the same long-studied laws of exposure and interchangeability. Along with the continuous improvement of designs and increasing accuracy of cameras, standardization and improvement of methods for constructing an image and its correct exposure. The International Organization for Standardization (ISO), the largest organization issuing recommendations and standards applied in various industries around the world, first released a standard for digital photography, which establishes the relationship between the magnitude of matrix signals and specific exposure indices in 1998. This played a role in unifying and bringing a large number of digital camera models produced after the publication of the standard to common principles for assessing exposure and photosensitivity, and avoided complications and confusion in methodology and terminology. This standard was a kind of SI digital photography. In 2006, the standard was improved and supplemented (revision of ISO 12232: 2006, confirmed in 2015 "Photographs. Digital cameras. Determination of exposure index, ISO sensitivity values, standard output sensitivity and recommended exposure index").

Given the standardization of exposure metering processes and bringing photography to common standards, as well as improving the accuracy of photographic equipment and image quality, the logical question is whether modern cameras can be used as not only event recorders, but also parameters of captured objects, both structural and brightness. Often, photographs are the only materials that can make it possible to evaluate certain parameters of the surface being shot, and the scarcity or malfunction of the equipment casts doubt on the possibility of measuring the albedo of the surface - a very important parameter in calculating the energy balance of the surface, the importance of which, in turn, cannot be overestimated. Digital photography provides the possibility of its practical application for determining the albedo of the removed surface.

The proposed invention relates the amount of exposure, the brightness of the scene and the incoming radiation. The photographic technique has a number of parameters that allow calculating, based on metadata (data on the shooting parameters) and image data, the brightness of the surface being surveyed (investigated).

By exposure in photography is meant the amount of actinic (i.e., acting only on the sensing element) radiation received by the photosensitive element. In the case of digital photography, this element is a photosensitive matrix.

For visible radiation, exposure H is expressed as the product of the illumination E (measured in lux) and the shutter speed t (measured in seconds) and measured in lux seconds:

The shutter speed t is controlled by the shutter of the camera, and the illumination E is directly related to the characteristics of the camera lens and its relative aperture. The relative aperture is the ratio of the diameter D of the entrance pupil of the lens to its rear focal length f '. It is expressed as a fraction:

.

.

With the numerator reduced to unity, the denominator of the relative aperture N is the diaphragm number. Obviously, the larger the aperture value, the smaller the relative aperture and, therefore, a smaller amount of light hits the sensor. Moreover, as is clear from equation (2), a change in shutter speed inversely proportional to a change in illumination allows you to keep the exposure unchanged. Those. an increase in exposure time and an increase in radiation power are interchangeable, and the same exposure H has the same effect on the photosensitive element. This is the law of interchangeability or the Bunsen-Roscoe law, discovered in 1859-1862. (see. Kantselenbogen E.D. Photokinotechnics: Encyclopedia, Editor-in-Chief E.A. Iophis. M .: Soviet Encyclopedia, 1981).

Upon a more detailed consideration of formula (2), it becomes obvious that the amount of illumination E, which depends on the characteristics of the lens, also depends on the brightness L of the captured object (the studied surface). This means using multi-segment metering, which measures the overall brightness of the entire scene being shot (since spot or center-weighted metering only measures the brightness of a specific area). Thus, the disclosure of the illumination E as a value depending on the brightness L of the object (in cd / m ² ) and the characteristics of the lens, described by the coefficient q, with aperture number N and shutter speed t, allows us to express the exposure H and equation (2) in the form of the equation:

.

.

The coefficient q characterizes the parameters of the lens and is a dimensionless quantity that "collects" the main parameters of the lens. It describes the cumulative effect of vignetting, light transmission, etc. Data on these characteristics can be obtained either from the technical passport of the product (where they are published), or by the method of calculation and measurement. The coefficient q can be calculated through the equation:

, где

where

T is the transmittance of the lens, υ (θ) is the vignetting coefficient of the lens, θ is the angle relative to the optical axis of the lens. Most often, q = 0.65 (at T = 0.9, υ = 0.98, θ = 10 °), however, with known lens parameters that may be in the public domain (set by the manufacturer), we can calculate the value of the coefficient q for any particular case with high accuracy. In the absence of data on the coefficient q, it can be calculated empirically from a picture of a surface of known brightness.

One of the differences between digital and analog photography, in addition to instantly obtaining a digital image, is the ability to receive, at the same exposure, images of varying degrees of brightness (which can be compared with a film whose sensitivity varies according to the will of the photographer). This is achieved by changing the photosensitivity of the camera’s matrix, which is reflected in a change in the preliminary amplification of the electrical signals from it and their conversion into the sRGB color space (this color space is regulated by the ISO 12232: 2006 standard). The relationship between the color space parameters and the signals from the photosensitive matrix is set by the manufacturers and is called the exposure index. Its values are selected in such a way that, with equal shooting parameters and the resulting digital and analog images, the film sensitivity corresponds to the same image. For this reason, the exposure index in digital photography is called the equivalent ISO sensitivity.

In fact, following the manufacturers of photographic equipment to the established standard means that with the same shooting settings for the same scene (lenses comparable in characteristics, the same photosensitivity and shutter speed settings), you can get the same image in brightness from different cameras. The vast majority of shots on different models of photographic equipment (photo-recording devices) made on the same settings will have comparable brightness and similar image characteristics. This makes it possible to estimate the brightness L of the investigated surface (object) based on the brightness of the image (taking into account all the specified shooting parameters). However, even with the given reference (accepted as reference) shooting parameters, due to the technical imperfection of the photosensitive elements and the narrowness of their dynamic range, as well as the possible non-linear measurement of brightness within the color space and large differences in the brightness of the scenes taken (due to the difference in illumination , and due to the difference in the characteristics of the objects being shot), it is possible to “dip” the darkened areas into black and light ones into white, i.e. their over- or underexposure, in which the interpretation of images will be difficult due to their non-representativeness, since extreme values will prevail over real ones. This can be circumvented by changing the shooting parameters depending on the illumination and normalizing according to these changes, however, this significantly complicates the task of processing and interpreting the results.

At the same time, the automatic settings of the camera almost always produce an image of approximately the same brightness, which allows us to solve the modified problem of determining the brightness of the object, knowing the exposure algorithm (i.e. how the camera determines the necessary brightness of the image) and shooting parameters.

The ISO 12232 standard establishes the relationship between the magnitude of matrix signals and specific exposure indexes, and offers photographic equipment manufacturers five methods for determining specific exposure index values:

- The REI methodology of the recommended exposure index is the only technique applied to color spaces other than sRGB and allows manufacturers to independently decide at what exposure index values the image is correctly exposed.

- Two techniques based on the signal-to-noise ratio are most often used in amateur photographic equipment.

- The technique of the saturation point, which is based on the maximum brightness of the image and selects the exposure index so as to avoid overexposure of areas of the image.

- The method of standard output sensitivity, according to which the average level of image brightness is taken to be that when shooting a gray card with 18% reflectivity when changing the exposure with an exposure system calibrated according to ISO 2721 without using exposure compensation.

In the case of the REI method and signal-to-noise methods, determining the brightness of an object from shooting parameters is possible only if a large sample of images of surfaces of known brightness with known shooting parameters is accumulated and the dependencies between them are subsequently calculated, since these data are difficult to find in the public domain. This imposes restrictions on the identification of the relationship between exposure and equivalent photosensitivity.

The saturation point technique and the standard output sensitivity technique seem to be the most promising for calculations and rely on simple laws regulated by the standard.

So, for a saturation point technique, the exposure index (equivalent light sensitivity S) is determined by the formula:

, где

where

H _sat - maximum exposure, which does not lead to overexposure and the appearance on the image of areas that are “embossed” in white.

For the standard output sensitivity technique, the equivalent photosensitivity S is determined by the formula:

, где

where

H _sos is the exposure equal to 118 in an 8-bit image in the sRGB color space, corresponding to the display of a gray card with a gamma correction of 2.2.

As can be seen from equations (6) and (7), these two methods are very close, and the transition from calculating the surface brightness according to one technique, according to the thesis of the manufacturer applying this technique to another technique, will not be difficult. In more detail, the methods and reasons for establishing the coefficients of 10 and 78 in the numerators of the equations are described in the standard ISO 12232: 2006.

Consider the applicability of the standard output sensitivity technique to determine the brightness of the surface being taken, guided by the assumption that it is most often used in modern photography, in comparison with the saturation point technique.

This technique, in fact, relies on the Ansel Adams zone system, formulated in 1939, according to which any illuminated object can be divided into 11 zones (from 0 to 10) in brightness from brightest to darkest. The middle is the fifth step of the scale, describes a standard gray tone (having a reflectivity of 18%) (I. Ilyinsky, Zone Exposure System, Photomagazine magazine No. 1-2, 1998, pp. 94-98. ISSN 1029-609-3).

According to equation (7), and knowing the photosensitivity on which the picture was taken, we can calculate H _sos :

Given equation (4), we can obtain the following equality:

, из которого следует, что яркость объекта съемки (яркость снимка исследуемой поверхности L') (в кд/м²) равна:

, from which it follows that the brightness of the subject (the brightness of the image of the investigated surface L ') (in cd / m ² ) is equal to:

, где G - коэффициент методики экспозиционного индекса, равный 10 (десяти) для методики стандартной выходной чувствительности, и равный 78 (семидесяти восьми) для методики точки насыщения, или имеет другое значение для других методик, выбранных производителем фототехники.

, where G is the coefficient of the exposure index technique, equal to 10 (ten) for the standard output sensitivity technique, and 78 (seventy eight) for the saturation point technique, or has a different value for other techniques selected by the photographic equipment manufacturer.

From the obtained formula (10), it can be seen that to recalculate the brightness of an object using the standard output sensitivity technique or the saturation point technique, it is enough to replace the coefficient 10 in the numerator with 78 and vice versa.

Determining the brightness of an object based on the shooting parameters is a very important step for calculating the regression equation that relates the shooting parameters and the albedo. However, the survey takes a certain amount of time, during which many parameters can affect the illumination, for example, the transparency of the atmosphere, the elevation of the sun above the horizon, etc.

Total radiation is a parameter that allows you to take into account the change in illumination and obtain correct albedo calculation data in various conditions (conditions) using one pre-calculated equation (instead of calculating a new equation for each specific case). Measurement of its flow is a fairly simple task that can be solved using actinometric equipment, for example, meteorological pyranometers and a conventional multimeter / voltmeter, or more advanced systems (for example, data loggers).

In addition to the variable influence factor of the incoming radiation, there is an error caused by a non-systematic exposure meter error. In fact, if you look at the pictures of surfaces, you can see that they are close in brightness, but not absolutely identical. To eliminate errors in the calculation of normalized brightness, it is necessary to calculate the brightness of each image (for example, in Adobe Photoshop).

In the context of the above, we can imagine the albedo as a function of the total radiation Q and the normalized brightness L:

.

.

And if the value of Q is already known from measurements and does not require complex calculations, then to calculate the value of the normalized brightness L, simple calculations are necessary.

The neutral gray color in RGB space corresponds to a brightness of 128 - relative to this value, denoted by l ₁₂₈ , and the normalization coefficient K is calculated for the exposure metering error:

, при этом l_n - яркость снимка в пространстве RGB (может быть получена в любом редакторе), l₁₂₈ - средняя яркость снимка в пространстве RGB.

, while l _n is the image brightness in RGB space (can be obtained in any editor), l ₁₂₈ is the average image brightness in RGB space.

Then the value L of normalized brightness is calculated by a simple equation:

,

,

After receiving for each observation the calculated values of normalized brightness and total radiation, the albedo values are obtained by solving the equation:

To initially verify the results of theoretical studies, ice was shot on an iPhone 5c phone model with parallel measurements of incoming radiation using a Yanishevsky pyranometer, the readings of which were recorded with a multimeter. The simplest technical means were deliberately chosen. Measurements were carried out in mid-March 2015 at an ice test site on Lake Onega in the area of Petrozavodsk. The landfill size was 90 meters by 40 meters, the grid between measurements was 10 × 10 meters, the survey numbered 49 pairs of measurements. Data collection was carried out by devices held by hands and located at a distance of 1.5 meters from the ice surface, the horizontal plane II of the sensitive element of the pyranometer 2 was provided with a gimbal.

In the absence of data from the manufacturer, it was assumed as an assumption that the camera’s exposure index determines the phone’s standard output sensitivity method, since the brightness of the pictures was close to neutral. After calculating the normalized brightness of the removed surface and the total radiation flux, the multiple regression equation was calculated in the Statsoft Statistica software product (the coefficients were: α = 0.0025, β = -0.0304, γ = 28.5917):

.

.

The applicability of this equation to other measurements by other cameras requires verification, since it is possible that the exposure index of the phone’s camera was determined by the signal-to-noise method rather than the standard output sensitivity. However, normalizing the brightness of the image is designed to level out possible errors caused by exposure metering of the camera.

The coefficients of the equation for a specific equipment are refined if the selected equipment at the preparatory stage was shot reference surfaces with known albedo parameters. Moreover, to calculate the coefficients α, β, γ of the multiple regression equation by the selected equipment under the expected conditions and in the selected modes, materials are collected on reference surfaces (surfaces whose albedo value is known or previously measured in the usual way). Survey of reference surfaces and calculation of the coefficients α, β, γ can be performed at any stage prior to the final albedo calculations.

The brightness of ice, obtained by calculation according to the above formulas, ranged from 500-4000 Cd / m ² (these values predictably changed after normalization and obtaining a synthetic value of normalized brightness), which looks pretty reliable.

Nevertheless, even with incorrect values of the calculated brightness of the object, the obtained linear regression equation may be valid for calculating the albedo from the images of this model of the camera installed in the telephone.

Perhaps a qualitative improvement in the accuracy of determining the albedo when selecting the correct pair of camera-lens and the correct method of calculating the exposure index technique. The accumulation of data on this topic can make it possible to clarify the coefficients of the calculated dependence between the shooting parameters, calculate the correction coefficients for specific pairs of camera-lens, or the individual equations of communication between the shooting parameters and the albedo for specific equipment samples.

The following are possible simplifications of the methodology aimed at a slight reduction in the calculations, or an increase in accuracy for a specific series of observations.

The first simplification is based on two points:

- taking into account the total radiation in the calculation of the normalized brightness of the object;

- a linear relationship between albedo and normalized brightness (in this case, the linear regression equation is simplified, in which the coefficient β is taken equal to zero).

This implies a slight change in the calculation of L (13), supplemented by one member:

.

.

In the presented equation, Z is the normalization coefficient for the radiation flux equal to:

, где

where

Q _n is the total radiation at a particular moment at a particular point in the image; Q _norm ^{_ is} assumed to be 500 W / m ² and expresses an approximation to the radiation flux at moderate latitudes in spring / autumn with a cloudless sky.

For calculations, data from the same series of 49 observations considered above were used. After calculating the normalized brightness of the surface being removed, a calculation was made of its correlation coefficient with the surface albedo. The calculation was performed in the Statsoft Statistica software product, the calculated correlation is significant and amounts to 0.90.

The linear regression equation calculated for this pair of devices is as follows:

.

.

FIG. 4 illustrates a graph of linear albedo regression and normalized brightness of the subject (test surface) according to the experimental data.

The second simplification implies the possibility of calculating the linear regression equation immediately before measurements based on the obtained data of “calibration” images of surfaces whose albedo is known. In this case, it is possible to use coefficients for normalizing the brightness of the image, equal to 128, and the radiation flux equal to not 500 W / m ² , but relative to the average values during the observation and shooting. Theoretically, this may make it possible to obtain more accurately calculated albedo values, however, the linear regression equation in this case will not work in excellent lighting conditions (i.e., a new calculation will be needed for another series of measurements).

For calculations, data from the same series of 49 observations considered above were used. After calculating the normalized brightness of the surface being removed, a calculation was made of its correlation coefficient with the surface albedo. The calculation was carried out in the Statsoft Statistica software product, the calculated correlation is significant and also amounts to 0.90.

To compare the accuracy of the methods, the albedo values were calculated. The graph of variability of the observed and calculated albedos at different points of the polygon is shown in FIG. 5.

Observed Albedo - The albedo that was measured at the point of the polygon.

The calculated albedo is the albedo calculated according to the multiple regression equation (14).

Calculated albedo II — albedo calculated according to simplification to linear regression to equation (17) with normalization to the average image brightness of 128 and a radiation flux of 500 W / m ² .

Calculated albedo III - albedo calculated according to simplification to linear regression to equation (17) with normalization relative to the average observed brightness and radiation flux.

As can be seen from FIG. 5, all methods provide fairly reliable data on albedo. Moreover, the non-simplified method (with the exception of points 2 and 37 of the polygon) demonstrates the greatest accuracy, and the simplified methods (second simplification) do not provide the expected increase in the calculation accuracy.

The proposed solution to relate the measured brightness of an object, total radiation and albedo to multiple regression is so simple and obvious that it can be said to lie on the surface. The convenience of the method lies in the fact that when it is used, it is possible to choose from a wide range of equipment in order to use the most suitable one. Knowing the parameters of the lens and the lens-camera bundle, one can easily calculate the linear regression equations to relate the brightness of the scene and the albedo. In this case, you can choose wide-angle lenses (for areal estimates), or telephoto lenses (for more detailed estimates of specific fragments of surfaces).

As the example above showed, shooting can even be carried out on the phone, and, despite the fact that the choice of photosensitivity on the phone is most likely determined by the signal-to-noise ratio, and the obtained values of the normalized brightness of the shot scenes could slightly differ from the real ones, the calculated equation ( 14) multiple regression allowed to obtain albedo data very close to real.

Flexibility in the choice of equipment allows you to implement measurements with a small set of necessary technical means - this, in turn, provides the opportunity to use specific equipment bundles on specific media. On ships of the ice class, passing through the ice fields, it is possible to install larger and more precise instruments on the remote rod for a more detailed ice survey. On unmanned aerial vehicles (UAVs) you can put light cameras with lenses that have a small focal length (for areal estimates) or a large focal length (for point estimates).

Most likely, the most accurate results, the total mass, oddly enough, will be obtained on the simplest cameras of compact cameras and telephones, and the like. A wide range of lenses for system cameras implies the need to take into account the characteristics of each specific lens model. So, if for simple cameras the approximation that the coefficient q = 0.65 allows us to obtain reliable data, then in the case of system cameras equipped with different lenses, this assumption can cause significant errors. This means that in calculations it is necessary to take into account the q factor suitable for a particular lens, and even for specific shooting settings. When using high-aperture lenses on system cameras, it is recommended to use aperture priority modes with settings in which the aperture of the lens is closed - this allows you to neutralize the effect of vignetting, typical of many high-aperture lenses, on the brightness of the image and on metering. The coefficient for a particular lens-camera bundle or a specific camera model can be clarified by knowing the brightness of the scene being shot (for example, using a brightness meter or spotmeter). Then, with other things known from the equation of the inverse (13), its value will be equal to:

, где

where

L is the known (measured) brightness of the scene.

It is also worth considering that many lenses for system cameras equipped not with an electronic but with a mechanical aperture control drive (for example, Pentax K or Nikon F system lenses) may have an error in setting the aperture value. In practice, this means the difference between the set f-number and the actual relative aperture, which leads to an incorrect determination of the brightness of the scene being shot.

In any case, a preliminary calculation of the q coefficient or the use of the known one, the calculation of the multiple regression equation for a particular camera, or a lens-camera bundle, is a desirable and sometimes necessary condition for ensuring the accuracy of measurements. Calculation of q from equation (18) can give an incorrect value of the coefficient, however, this value eliminates the above-described errors of the photo equipment or exposure method.

Description of the methodology and recommendations

For the selected equipment bundle, a step-by-step description of the proposed methodology is given below.

Preparatory stage:

- select equipment and intended settings. The kit necessarily includes two elements: a photo-recording device 1 (for example, a conventional camera), which will be used to photograph the surface, and an actinometric device 2 (for example, a pyranometer), which will measure solar radiation.

For cameras 1 with zoom lenses, it is recommended that you select the focal length for shooting and adjust the shooting mode and metering. If the equipment allows you to select the aperture priority mode, then select it by setting the aperture to a fixed value. A center-weighted exposure metering mode is preferred.

- If the coefficient q is unknown, then use equation (18) when shooting a target of known brightness for its calculation. If its calculation is impossible, take q = 0.65. Errors in determining q will lead to errors in determining the brightness of the object.

- Refine (calculate) the multiple regression equation of the form (14) according to the control images of the reference target (s) / surface with a known reflectivity and registration of total radiation data. To achieve the best final results, it is necessary to shoot reference surfaces in the modes, conditions and shooting distances assumed at the data collection stage (close to those planned for data collection). Such surfaces can be objects and planes with previously known (or measured in the usual way) albedo parameters. In the future, this will allow reconciling the coefficients of the final regression equation.

After that, the selected set of equipment is ready for use.

Data collection stage:

- Deploy and install equipment. Set the equipment settings as in the preparatory phase.

- Check the accuracy of the equipment installation. It is desirable that the horizontal and mutual parallelism of plane I of the test surface, plane II of the sensing element of the actinometric equipment 2 (device) and plane III of the photosensitive sensor (element) of the photo-recording device 1 (camera) be observed (Fig. 1).

- Proceed to data collection. For data collection, a photo-recording device 1 and an actinometric device 2 are used. When collecting data, it is necessary to ensure the highest possible compliance with the horizontal and mutual parallelism of the investigated surface (its plane I), plane II of the sensing element of the actinometric equipment 2 and plane III of the photosensitive sensor of the camera 1 (and perpendicularity optical axis of the IV lens). The mutual parallelism of these planes with the plane of the removed surface provides the best accuracy of the results obtained, therefore, the method will show itself best when measuring the albedo of surfaces with no or minimal slope.

- In the process of data collection, ensure their synchronous (simultaneous) acquisition so that each measurement from the actinometric equipment 2 corresponds to a measurement / image from the photographic equipment 1 (the surveyed surface is taken and the total radiation Q (data on the incoming radiation) is measured simultaneously).

Analysis Stage:

- According to the collected data, using equations of the form (13) and (14), calculate the albedo values of the underlying surface.

The preparatory stage can be skipped when reusing a set of equipment: once the coefficients and equations calculated for it can be used for all subsequent measurements on the selected settings and modes in similar conditions. This significantly reduces time loss.

An example of using the method of remote measurement of albedo using photo-recording equipment.

The verification of the method for remote measurement of albedo was carried out in March 2015 at an ice training ground located on Lake Onega in the area of Petrozavodsk. The aim of the study was to measure the albedo of the ice surface by the proposed method.

All work was carried out in the daytime in cloudless conditions. The ice surface is smooth, sometimes snowy and fractured, without hummocks (Fig. 2).

The equipment that was intentionally chosen was the simplest technical means for which not all parameters are known (for example, G and q coefficients) in order to demonstrate the flexibility of the method and the possibility of obtaining high-quality data even under strong assumptions, in adverse equipment conditions:

- Pyanometer Yanishevsky M80 (as actinometric equipment installed on the site) with a multimeter-voltmeter for voltage recording;

- A common iPhone 5c phone model (as photometric equipment).

03/16/2015 ice surveys were carried out at the ice training ground. Ice was shot at control points with known albedo parameters measured using an M80 pyranometer. At the same time, various types of surfaces were chosen: snowy, with compressed snow, fractured, smooth, etc. As control points, ordinary polygon points were selected. This was dictated by the need to perform a subsequent comparison of the observed and calculated albedo data.

When collecting data, the ice surface was shot at the camera from a height of 1.6 m with the highest possible horizontalness. The pyranometer was at the same height; the instrument was horizontally secured by a gimbal.

The total number of points at which measurements were taken is 49 (one observation was rejected due to an imperfect photograph).

At each point for verification, additional measurements of the total and reflected radiation were carried out in the usual manner described in the Guide to Hydrometeorological Stations for Actinometric Observations. - L .: Gidrometeoizdat, 1973. The measurements were recorded in a field notebook.

1) Based on the data from the survey of control points, the albedo value was calculated.

According to the data of the multimeter connected to the M80 pyranometer, the values of the total and reflected radiation were obtained. The conversion factor of the selected instance of the M80 pyranometer is 100, thus:

Q = 100 * uV,

where uV - multimeter readings in millivolts.

The observed albedo is equal to the ratio of the radiation flux reflected from the surface to the flux that has fallen on it

2) according to the images, the brightness L 'was calculated:

Where G - was taken equal to 10, as for the standard output sensitivity technique, since the manufacturer did not disclose information about the chosen exposure index method, q is unknown, and was taken equal to 0.65, aperture number N, shutter speed t, equivalent photosensitivity S - are known and derived from snapshot metadata.

In the Adobe Photoshop software product, data were obtained _ln average brightness of images in the RGB space, which allowed us to calculate the normalization coefficient for exposure metering error.

After that, the normalized brightness value L was calculated:

L = L'K _exp

3) Based on the calculated and received data of the total radiation, normalized brightness and measured at albedo control points, the coefficients of the multiple regression equation were calculated in the Statsoft Statistica software package:

A = αL + βQ + γ,

where α, β, γ are empirical coefficients for the selected equipment and shooting conditions. In our case (the Apple iPhone 5c smartphone, with the assumption that the camera’s exposure index determines the method with standard output sensitivity q = 0.65 and the Yanishevsky pyranometer when shooting the ice surface from a height of 1.5 meters), their values were: α = 0.0025; β = -0.0304; γ = 29.5917.

4) Using the obtained multiple regression equation, based on the measurement data of the total radiation and photographs, the albedo was calculated at all points of the polygon.

5) Since, to control the accuracy of the method, parallel albedo measurements were made using a pyranometer, sequentially directed up and down, the observed and calculated albedo data at the points of the polygon were compared. FIG. 3 illustrates the spatial variability of the albedo observed and the albedo calculated using the proposed method.

The correlation coefficient between rows A of the observed and A calculated, calculated in the software product Stotsoft Statistica, is 0.92. The standard error of estimate is 2.65.

FIG. 3 illustrates the possibilities of applying the method using the simplest available devices based on a sample of 49 points. The increase in the sample should favorably affect the accuracy of the method. It is worth noting that this sample was recruited within about one hour. Thus, the short stage of surveying surfaces with a known albedo (in our case, we recognized it by instrumental observations right there, on the spot) allows us to subsequently accumulate the volume of the data array covering a large area, especially if we automate the process of collecting and recording data and establish equipment on the vehicle.

If we talk about a comparison with conventional methods for measuring albedo, it must be mentioned that measuring albedo with traveling albedometers imposes a number of limitations related to:

- the inertia of the pyranometer, which leads to a longer duration of one measurement;

- a drop in accuracy associated with a possible difference in conditions during the reading of the total and reflected radiation (the appearance of clouds, etc.);

- the need for accurate installation and alignment of distances from the surface to the instruments.

At the same time, the proposed method allows for the registration of data in an almost automatic mode by improvised means, with parallel photographing of the surface. This allows you to obtain additional data on the state of the underlying surface, which can be of great value per se, and perform the rejection of measurement points for which data recording conditions were not met for one reason or another. Due to the constant measurement by the pyranometer of the total radiation and its constant position (up), the influence of the inertia of the device is minimized, which significantly reduces the time of each measurement.

The advantages of the proposed technical solution are as follows:

- the ability to choose equipment from a wide range of products for specific needs and for specific carriers (UAVs, ships, in situ measurements on foot). It can be used for a large set of equipment with different characteristics (different camera models, different shooting heights, lenses with different EGFs and, as a result, different coverage of the rented area);

- the reality of remote albedo measurements by instantaneous measurements without stops using simple meteorological instruments and a camera;

- cost-effectiveness - for most tasks and solutions, the proposed method provides a significant reduction in the cost of obtaining data in comparison with the possible use of industrial photometers and projection bright meters, which, moreover, do not provide instant data;

- the ability to continuously refine the survey results - empirical coefficients for each set of equipment, as the accumulated data of conventional measurements and measurements by the selected method, can be refined and recalculated, increasing the accuracy of all data collected by this equipment;

- receiving along with measurements of visual data (photographs) that provide additional information (physical properties of the surface being taken, snow, pollution, shakeiness, presence of streaks, etc.) for analysis, as well as the possibility of filtering and deleting unrepresentative data from the data of the images and emissions that reduce the reliability of the resulting array of information;

- development potential when using cameras of different spectral coverage;

- the potential for replacing photo-recording equipment with bright meters;

- low complexity of determining the albedo of the studied surfaces, reducing the time required to collect data on the studied surfaces due to the absence of the need to stop to take measurements (which is dictated by the lower inertia of the photorecorder compared to the pyranometer, and is most pronounced on surfaces with high variability of properties on small spatial scale), as well as reducing the number of necessary operations to determine the albedo (i.e., it is enough to make survey the surface, measure the total radiation in its area and perform simple mathematical calculations), while there is the possibility of automated data collection on the surfaces under study and their processing.

However, there are a number of difficulties that must be considered when using the method.

Thus, the disadvantages include the need for control measurements to calculate empirical coefficients in case of changing conditions for data collection, as well as the need to take into account the technical features and possible imperfection of the selected samples of photo-recording devices.

In addition to conventional multi-zone, center-weighted, and spot metering, matrix metering has recently begun to be added to cameras. Its exposure determination algorithms are different from the “classic” ones, so calculating the relationship between the brightness of the scene and the albedo can be difficult. If the matrix metering on the camera replaces multi-zone metering, you can use center-weighted metering. According to it, the central third of the frame will have a strong influence on the exposure estimate.

It is also worth considering the possibility of the influence of glare and flare. In order to avoid this, it is recommended to use lenses with lens hoods. In turn, hoods can affect the vignetting coefficient. In addition, the use of filters can also affect the accuracy of determining brightness, since they can affect the transmittance of the lens-filter bundle and vignetting. However, their application also provides the potential to use the camera for shooting in specific ranges of the spectrum. For example, knowing the spectral coverage of the camera sensor and the spectrum blocked by the filter, it is possible to obtain images in the infrared (IR) or ultraviolet (UV) range on some equipment bundles.

In addition, it is important to understand that the accuracy of the installation of equipment can have a significant impact on the accuracy of calculations: the non-parallelism of the planes of the incoming radiation sensor, camera sensor and the removed surface can lead to a significant error of the results.

When shooting surfaces, for correct calculations, it is worth checking carefully all camera settings to avoid accidentally entering exposure compensation or other changes affecting the exposure and brightness of the resulting image.

Another important circumstance that should be taken into account is that many manufacturers of consumer photographic equipment overestimate the photosensitivity values of matrices installed inside cameras. So, for example, according to the DXO laboratory, the declared photosensitivity of the Nikon D610 camera, equal to 100 units, correspond to real 74 ISO units.

The best results when using the method can be obtained on flat surfaces and surfaces with a minimum slope, such as ice fields, tundra. The effect of surface roughness and the scale of the survey requires further detailed study.

All of the above allows us to argue about the great potential of the technical solution, which consists not only in the possibility of using albedo for measuring, but also in the design of albedometer devices based on the proposed principles, with the possibility of installation on various carriers (UAVs, ship, wearable), which will provide quick and high-quality data collection over large areas.

Claims (17)

1. The method of determining the albedo of the surface, which consists in the fact that using the actinometric device measure the total radiation Q in the area of the test surface, characterized in that they determine the brightness L of the test surface and determine the value of the albedo A of the test surface by mathematical dependence: A = αL + βQ + γ, where α, β, γ are the coefficients of the regression equation. 2. The method according to p. 1, characterized in that the coefficients of the regression equation α, β, γ are determined by calculation based on the results of determining the brightness of the reference surface with a known albedo and measuring the total radiation in the area of the reference surface. 3. The method according to p. 2, characterized in that the brightness of the reference surface is determined using a device for measuring brightness or using a photo-recording device. 4. The method according to p. 1, characterized in that the coefficients of the regression equation α, β, γ are determined by mathematical modeling. 5. The method according to p. 1, characterized in that the brightness L of the investigated surface is determined using a device for measuring brightness. 6. The method according to p. 1, characterized in that the brightness L of the test surface is determined by shooting it using a photo-recording device, while the brightness value L is determined by the mathematical dependence: L = L'K _exp , where K _exp is the normalization coefficient equal to l _n / l ₁₂₈ , where l _n is the brightness of the image in the RGB space, l ₁₂₈ is the average brightness of the image in the RGB space, equal to 128; L 'is the brightness of the image of the investigated surface, equal to GN ² / qtS, where G is the coefficient of the exposure index technique; N is the aperture number of the photo-recording device; q is the coefficient characterizing the parameters of the lens of the photo-recording device; t is the shutter speed of the photo-recording device, s; S is the equivalent photosensitivity of the photo recorder, ISO units. 7. The method according to p. 6, characterized in that the surveyed surface and the measurement of total radiation Q in its area are carried out in compliance with the horizontal and mutual parallelism of the investigated surface, the planes of the sensing element of the actinometric device and the photosensitive element of the photo-recording device. 8. The method according to p. 6, characterized in that the surveyed surface is surveyed and the total radiation Q is measured simultaneously.

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