Measurement of Visibility by Photographic Photometr CARSTEN STEFFENSI Stanford Research Institute, Stanford, Calif,
A method has been developed for measuring pkstegraphically the extent to which visual range has been reduced by haze. Black objects that are far enough away to be partially obscured are photographed; the photographic densities of the images of the objects and of the adjacent sky, if it can be seen, are measured on the negative. The visual range is calculated from these densities, as are the distance of the object and the contrast of the film. The errors to be expected by the method, if the horizon sky can be used as one object, are less than 10% with readily available equipment and can be reduced to 2% with increased expense and care.
where b is the coefficient of attenuation a t the point z, and cc is a scattering coefficient, a t the point 2. The only physical situation of practical importance in this research is that where both the illumination on the aerosol and the characteristics of the aerosol are substantially uniforri along the light path, Then k and n are constant an4 Equation 2 reduces
to: d = ce-k'
+ u/k
(3
where e is a constant of integration h a t involves the opticai abararteristics of the object
Incident
A
iHurnination
TMOSPHERIC pollutsnts on the west coast are mually mixed with the natural haze that is so striking a feature of
the landscape there, Ear from any source of human contamination. It is therefore necessary in studying such pollution to find ways of distinguishing polluted haze from natural haze and of measuring the increase in haziness that is caused by the pollution. The optical characteristics of the haze may be expected not only to lead to such results, but also to give some indication of the physical oharacteristics of the aerosol. Moreover, the visual range, which i s one such characteristic and which is ordinarily estimated from the ease with which known objects can be seen, is of obvious interest as a quantitative measure of the intensity of the haze. Unfortunately, as ordinarily defined (9) and estimated, the visual range varies so much with the personal predilections of the obBerver that the estimates are not precise enough for these purposes even when the observations are made by trained and experienced personnel and the results of untrained observers are nearly valueless. The method that is presented in this paper consists of photographing a section of the landscape and measuring on the negative the relative optical densitics of the images of suitable objects. From these data, together with the photometric characteristics of the negative and the distance do the objects chosen, the visual range can be calculated.
X
Figure 1, Change of Light Intensity in Traversing an Illuminated AeroeoE
Camera
THEORY
Object I
Consider a length, dx, of the light path from the object 'to the observer through an aerosol (Figure 1). The intensity Z of the light flux from the object per unit cross section of the path will be decreased by some small fraction of its intensity at the beginning of the distance, dx,because of scattering and absorption, and will be increased by the additional light that is scattered in the direction of the observer by the suspended material that is in the length, dz, of the path, if that material is illuminated by the sura or other sources The differential equation for the change of intensity of the light with distance is, therefore,
d I / & = -kI 4-a
I
Figure 2. Arrangement for Measuring Effect of Haze, Using the Horizon Sky as One Object
(I1
ce-fkdr
i. e-SkdJ: J a e S k d d z
It is sometimes preferable to replace the eonstants c and (E of Equation 3 b y others that are more easily interpreted in terms of the observations. For an object at distance 8 , under conditione uniform both from the observer to the object and for a sufficient distance beyond (Figure 2), Equation 3 becomes:: ( I * - - I m )=
The integral of this equation is:
I =
s --.
@I
or
Present address, University of New Mexico, Albuquerque, N. M,
2396
(Io--d,PP---k8
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INDUSTRIAL AND ENGINEERING CHEMISTRY
November 1949
where I , is the intensity of the light in the direction from the object, a t the observer’s position; I , is the intensity from an infinitely distant object in the same direction a t the same position (in practice, the intensity from the horizon sky next to the object is used for I,); and ZOis the intensity in the same direction a t zero distance from the object. A case of especial simplicity arises when a black object is available, for then 10= 0 and:
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Measurements sometimes have t o be made over relatively short total distances because the layer of haze that is observed would otherwise be nonuniform, because it is desirable to sample the haze along the observed path or because of physical restrictions imposed by hills, buildings, or other obstructions in the vicinity. Furthermore, no suitable objects may be available. The most satisfactory method thus far found is then to construct two black objects, which are set a t fixed distances from the observer (Figure 3). Equations 3 or 4 and 8 then lead to:
r
*
This case of a black object against the horizon sky is the ideal that is approached a s closely as practicable in selecting objects for estimating visual range by the Weather Bureau. If the least fractional difference in intensity that the eye can perceive is e, and the distance of a black object that has just reached this contrast is v, the visual range, then
I--,
-re
(7)
I m
and 1 k
v = -In l/e
where M = In l / c ; the other new symbols are defined in Figure 8, Since Equation 11 cannot be solved algebraically for v, a table of values of v as a function of I*/]*has t o be calculated for the particular values of s and t involved. This calculation is not a serious drawback, since the use of artificial objects implies a more or less fixed arrangement of apparatus. The more serious objection, which is common to all arrangements that do not allow a t least an approach to direct observation of I,, is that greater precision is required in measuring I,/Ztthan would be required in measuring I J I m to attain the same precision in v~
from Equation 6; also
from Equations 8, 5, and 6. Equation 9 is the working equation that is used in most measurements of visual range by this method, The ratio of the two intensities can be replaced by a ratio of the corresponding apparent brightnesses, in these and the following equations, if desired. The value of the psychophysical parameter E is affected by the conditions of observation-for example, by whether or not the two objects are next t o each other or slightly separated. Under the best conditions E is found to be about 0.02, but under the conditions commonly found in visual observations of the visual range (and with the additional requirement that the object be recognized) the value is closer t o 0.05. Wright (IO)and Lohle (6) propose using a standard visibility wherein E is defined as 0.02 for instrumental observations and visual observations are corrected to the value that they would have under the best conditions. If 6 0.02 is used by definition and instrumental observations are compared with the visual observations that are usually recorded, one must expect most of the visually observed ranges to be less than those measured instrumentally, The derivation given above is a conventional one ( 7 ) . It does not seem t o have been generally appreciated, however, that lo and I,, despite their obvious physical interpretation, are merely two constants to be determined in whatever way is easiest, and that these equations can be applied in situations where I Oor I , or both have no direct physical counterpart. All that is required is the measurement of a sufficient number of intensities and distances t o determine the constants. An extreme case, for example, is that where rieither a black object nor the horieon sky can be used. One procedure is then to measure simultaneously the intensities of light from an object along the same path a t three distances, the distances being selected so that xg 2 2 = 22 - zl. Then from Equations 3 or 4 and 8: \=
-
-
If 5 8 - z2 # 22 X I the equations are still soluble (numerically) for any particular example, but they cannot be reduced t o a simple from.
Black Objects
Camera
Figure 3. Arrangement for Measuring Effect of Haze, Using T w o Black Objects
Hulburt ( 4 ) and others (7) Rave adequately demonstrated the experimental validity of such equations as 9, using methods of physical photometry. It does not seem t o have been generally appreciated, however, how easily the needed intensity ratios can be obtained by simple photographic methods, provided the results are not needed immediately. This simplicity arises, of course, from that fact that the precision required is more than a power of ten lower than the methods of photographic photometry are capable of yielding. Duclaux (f) has measured the extinction coefficient of clear air by photographic photometry, but since he was concerned with the Raleigh scattering of air, he confined his work to long ranges and a strict use of the equivalent of Equation 9. The ratios of intensities are to be determined from photographic negatives. The density, D,of a negative is D = g y log E. where g and y are constants and E is the exposure, over the range of densities with which the method is usually concerned. Exposure is considered to be E = I f ( t ) ,wheref(t) is some function of the time that reduces to t if the reciprocity law holds. If only ratios of intensities on the same negative are involved, the function of the time cancels from the ratio regardless of whether the reciprocity law holds or not. Then
+
where DI and DZare the densities of the images produced by the fluxes 11 and Iz,respectively, and y is calculated from other density measurements on the negative.
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I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Figure 4. Photograph Taken with Hollow Square C u t from Neutral Gelatin Filter APPARATUS Little apparatus is required for this work. A camera, a positive gray scale or an aperture diaphragm or one of the modifications of the camera that are desciibed below for determining 7,a densitometer, and some means of measuring the distance to the object photographed are all that are required. Since the size of the image whose density is to be measured depends on the size and distance of the object and on the focal length of the lens, and since the minimum size of image that can be used depends on the characteristics of the densitometer, there is an interrelation among the specifications for the object, the camera, and the densitometer. The densitometer that b a s used for most of the work was a \I. eston photographic analyzer. This instrument measures the light transmission through a circle about a millimeter in diameter, but the diameter of the image on the negative must be ai, least 2 ml. for easy measurement. It is only about a tenth as sensitive as the laboratory-type densitometer, but is simple. rugged, operable by nonscientific personnel, cheap compared to laboratory-type instruments, and measures a smaller area on the film than others of its class. The Ansco Panda, a box camera without adjustments, gave satisfactory results when suitable objects, that subtended angles greater than about 1.3"at the camera, were available. Smaller objects require lenses of longer focal length than are built into the Panda. A more elaborate camera has greater flexibility, but personnel with greater skill are needed to operate it. Figure 4 was taken with a K-9 aerial camera that had a lcns of 15-inch focal length; this requires that objects subtend only 0.3" to give images of adequate size. I n the observational situation that led t o use of Equation 11, a campra was built around a lens of 34-inch focal length in order to make the black objects ( 2 feet square a t about 750 feet and 4 feet square a t about 1400 feet) small enough to be built and maintained easily. Since 17 ith any ordinary lens the illumination at the focal plane falls off rapidly toward the edges of the picture, it is necessary to find by trial what area of the negative is satisfactorily uniform n ith the particular camera that is used.
METHODS OF MEASURING Thr y of the film must be measured in order to use Equation 12. One method is to take a t least one picture, on each roll of film, of a series of objects of known relative brightness, such as a uniformly illuminated, positive gray scale. A second method is to include the gray scale in the field of view. This method is the preferred
Vol. 41, No. 11
one if, as in some applications of Equation 10, the intensities that are to be combined in a single calculation are measured on different negatives. The illumination on the gray scale must then, of course, be the same on the successive negatives and the images of the gray scale must be close enough to the center of the picture to be in the area of uniform illumination for comparison with the similarly placed images of the test objects. A third method is the commonly used one of imprinting a gray scale on the negative by a separate exposure. 4 fourth method is to take two pictures of the same scene in rapid succession on adjacent frames of roll film, a t the same shutter setting but different aperture settings, and compaie the densities of the images of the same objects in the two pictures. This method requires a comparatively high quality camera, for i t depends on the setting of the aperture diaphragm and the reproducibility of the shutter speed, as well as the assumption that the light transmitted by the lens is proportional to the area of the aperture. All four of these methods can be used with unmodified cameras that are generally available. In the sixth method, developed but not yet published by Ttubin (81, a hollow square, cut from a neutral gelatin filter of density 0.3, for example, is mounted on a sheet of clear acetate in the film-pack or cut-film adapter. Part of the picture is thereby made by light reduced in intensity by a known amount (Figure 4). The filter is so mounted as to frame the area of uniform illumination in the center of the negative, and to cover part of it. If there were any doubt about the exposure being on the linear part of the curve of the density against the logarithm of the exposure, or if several density ratios were t o be determined from the same negative, a strip of negative gray scale could be used instead of the single filter.
PRECISION OF THE METHOD h typical set of measurements of a picture on Super XX film developed by a commercial finisher might give densities of 1.01 and 1.10 for the images of a black gas-holder 1.5 miles away and of the sky next to it. The densities of the images of the sky through the reducing filter of density 0.301 and next to it might be 0.91 and 1.10~
Then y = (0% - Dl)/log (12/11)= 0.631
I J I m = log-'(lI, - Dm)/-( = 0.719 and v
= s
log (1/c)/log { 1/[1
-
( Z S / I m ) ]1 = 1.50 X 1.699/0.552
=
4.61 miles
The uncertainty in this result arises mostly from the uncertainty in the measurement of differences in film density, (D2 - Q). 4 difference in film density, as calculated from replicate measurements with the Weston photographic analyzer that was used, is uncertain by 0.01. Tracing the effect of this uncertainty through the calculation above, the resulting uncertainty in y is about 6.2% of y, or 0.039. The corresponding uncertainty in I J I - is 0.031 or 4.3% of I,/Im. The uncertainty in v that results from this uncertainty in I J I W is 0.41 mile or 8.9% of v. Since s can usually be easily determined with much more precision than this, and since E = 0.02 (to give the standard visibility of Wright and Lohle) is a defined constant for present purposes, this is the total error in v . Precision somewhat better than 10% of the visual range is sometimes desirable and may facilitate the measurements. The y of Super XX film can be increased t o about 1.0 by developing for a longer time or by using high-contrast developers. The uncertainty in the determination of v is then 0.23 mile or 4.8% of u in the example above. The highest y that can be obtained easily is about 4.0, by the use of contrast process film. The uncertainty of v in the example above is then only 0 13 mile or 2.770, but since the exposure is quite critical, the procedure is no longer routine and skilled personnel are required for the photography. The uncertainty in the visual range can be lowered markedly by using a laboratory-type densitometer, with which another significant figure can be measured in the density, but this refinement not only requires skilled operators, but also so greatly increases the cost of the equipment as t o raise the question of using other instrumental methods instead of photographic photometry. There is, moreover, considerable doubt as t o the usefulness of such
November 1949
increases in precision. The total error in v was referred (above) to errors in measuring a difference in optical density, but if these errors were reduced t o a tenth the size there assumed, such considerations of precise photographic photometry as the variation of y from point t o point on the film, which can be ignored in the present method, would become significant. Of still greater importance are the variations of conditions in the field, which limit the application of the method even at its present precision.
CONDITIONS FOR USE OF THIS METHOD
*
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INDUSTRIAL AND ENGINEERING CHEMISTRY
There are certain precautions that must be taken in using this method to ensure valid results. These precautions, which are concerned mostly with the state of the atmosphere and the characteristics of the object that is used, can readily be deduced by investigating the assumptions that were introduced in deriving the equations that are used. Since they have been discussed in some detail by Middleton (7) and Duntley (W), only those points that have caused some difficulty will be mentioned here. The atmosphere must be uniform along the optical path. If the visual range is more than 0.25 mile, it will usually be obvious that both the concentration and the composition of the aerosol change with height. For example, King (6) has shown that the atmosphere above Mt. Wilson on a clear day is nearly free from dust, haze, and other similar aerosols, which are confined a t that location, then, to the layers between sea level and 1 mile. It is important to bear this vertical distribution in mind, especially when considering the integration to infinity. Thus the use of Mt. Wilson as an object for observation from Los Angeles is rarely justifiable even when it can be seen, for the optical path to the sky beyond Mt. Wilson will not be limited by aerosols that are qualitatively like those that limit the visual range for an observer .on the street in Los Angeles. Nonuniformity is especially liable to be found when the optical paths are not horizontal, as in the illustration just described. A uniformly clouded sky usually leads to satisfactory observations. It is, however, necessary to be especially careful not to be misled when measuring the term Z m . The ground haze must be dense enough so that the clouds cannot be seen through it on the horizon, for a cloud on the horizon will usually have a brightness quite different from an infinitely thick haze. These restrictions (and the others discussed in the reference given) on measurements of the visual range do not apply to this method alone, but are concerned with the much more fundamental problem of defining visual range. There is no simple answer to the question of how far one can see through a haze that is itself markedly nonuniform or is not uniformly illuminated. One may be unable to see a building a mile away in one horizontal direction, although one can see a mountain range 20 miles away in another horizontal direction or a t an angle of 10” upward. There are also certain conditions to be satisfied by the objects for use in this method. The first of these is the same as that for objects that are to be used for visual observation: for accurate determinations during daylight hours, it is advisable to confine the choice of marks to black or nearly black objects against the horizon sky (7). Assuming that the object is black is equivalent to assuming that 10 = 0 in the equations above. The fractional ~ error in the visual range that arises from neglecting I Q / Iranges from 0.02 a t 1 8 / I a = 0.9 to 0.1 at 1 8 / I a = 0.4,if Io/I- is really 0.05. The objects that are used must evidently be quite dark if this term is to be neglected. The ratio I0/Im has been calculated by Foitzik (3) t o be half the albedo of the object, if the object is lit by a uniformly illuminating sky. Wright (IO)has shown that the visual range, under a clear sky, of a gray object of albedo 0.25, in the shade, against the horizon sky is over 98% of that of a black object. It appears from these authors that Z0/Zm is likely to be about one quarter to two thirds of the albedo for objects that are not in direct sunlight. Examples of satisfactory objects are foliage (albedo about 0.04) and black painted objects (albedo
about 0.02). Open doors or windows into the interior of buildings will often have an albedo of less than 0.01. For visual observation i t is well known that the object selected must subtend an angle between 0.5’ and 5 for satisfactory precision (7‘). Below 0.5” the optical defects of the eye cause significant errors by diminishing the apparent contrast, and above 5 the object affects the uniformity of illumination of the light path, The corresponding condition in the method described in this paper is that the image of the object on the photographic plate must be large enough to measure with the densitometer, yet the object must be small enough not to affect the light path. By using lenses of sufficiently long focal length, many objects that are unsatisfactory for visual observation can be used. Duntley (2) has shown that the edge effect and the ground-glass-plate effect refer only to the characteristics of the eye and are not objective effects that might vitiate measurements made on a photographic plate. O
O
APPLICATIONS The method outlined above can be used wherever daylight visual ranges are to be recorded for future use. The pictures themselves show whether or not the atmospheric conditions are such that visual range is significant; they are a permanent, impersonal record that can be interpreted a t a later time by anyone who is concerned. On the other hand, the delay in getting the results, inherent in a photographic method, precludes its use by the Weather Bureau, the airlines, or others who require an immediate description of atmospheric conditions. This method is also useful in investigating the composition of the atmospheric aerosols. One procedure is t o calculate the visual range that, according to laboratory data, would result from the contaminants that are found, and to compare this calculated visual range with the observed visual range to be sure that all of the important contaminants have been included in the calculations. This procedure, which requires that the observed visual range be known more accurately than is necessary for operating aircraft (as an example), is inuse and the results are expected to be published at a later date. A second procedure in investigating the composition of aerosols is to measure the intensity of the polarized and unpolarized components of the light as a function of the angle from a source of light and as a function of the wave length. These data can be interpreted b y the same theoretical methods as are used in astrophysics to find the composition of the dark nebulae. This procedure is still under development. I n most problems of atmospheric pollution, the material that restricts the visual range is already well known, but where this is not the case, then such methods as these can be used to find what material is responsible, so that the remedial measures can be efficiently selected and directed.
ACKNOWLEDGMENT Acknowledgment is due to the Smoke and Fumes Committee of the Western Oil and Gas Association whose financial support and encouragement for the study of the causes of smog in Los Angeles made this study possible.
LITERATURE CITED (1) Duclaux, M. J., J. phus. Radium, 6 ( V I I ) , 323-8 (1935). (2) Duntley, S.Q., J . Optical SOC.Am., 38,179-91 (1948). (3) Foitaik, L.,Met. Z., 49,134-9 (1932). (4) Hulburt, E.O., J . OpticaE SOC.Am., 31, 467-76 (1941). (5) King, L. V., Trans. Roy. SOC.(London),212 A, 375-433 (1913). (6) LBhle, A, Z.angew. Met., 53,71-82 (1936).
(7) Middleton, W. E. K., “Visibility in Meteorology,” 2nd ed., Toronto, Univ. of Toronto Press, 1947. (8) Rubin, Sylvan, Stanford Research Inst., unpublished. (9) Thiessen, A. H.,“Weather Glossary,” Washington 25, D. C.: U. S. Dept. of Commerce, Weather Bureau, 1946. (10) Wright, H.L., Quart. J . Roy. Met. Soc:, 65,411-42(1939). RECEIVBD March 7, 1848.
