PHOTOGRAPHIC DEVICE FOR ACCURATELY MEASURING FISH / iwarine Biological Laboratory] APR 1 f) 1958 WOODS HOLE, MASS. SPECIAL SCIENTIFIC REPORT- FISHERIES No. 228 UNITED STATES DEPARTMENT OF THE INTERIOR FISH AND WILDLIFE SERVICE EXPLANATORY NOTE The series embodies results of Investigations, usually of restricted scope, intended to aid or direct management or utilization practices and as guides for administrative or legislative action. It Is Issued In limited quantities for official use of Federal, State or cooperating agencies and In processed form for economy and to avoid delay In publication . United States Department of the Interior, Fred A. Seaton, Secretary Fish and Wildlife Service, Arnie J. Suomela, Commissioner PHOTOGRAPHIC DEVICE FOR ACCURATELY MEASURING FISH By Clifford W . Long Fishery Research Biologist and Raymond A. Arzylowicz Fishery Aid Bureau of Commercial Fisheries Special Scientific Report- -Fisheries No. 228, Wa shington, D . C . November 1957 ABSTRACT A photographic measuring device using two cameras and strobe illumination has been developed to improve the accuracy of salmon body measure- ments in the field. The optical theory is given and the device is described in detail. The technique includes calculating longitudinal distances from photographs. The device is considered accurate within + 0.05 centimeters when ideal subjects are measured. CONTENTS Page Introduction Theory Parallax error Special case General case Perspective error Description of device Photographic measuring device Base and framework Strobe light and power pack Camera assembly Automatic features Wiring Technique of use Taking the pictures Reading film Calculating longitudinal distances Calculation of OQ" Calculation of OQ" Calculation of Q'Q" Performance Portability Automatic features Efficiency Taking measurements Reading film and calculating longitudinal distances Accuracy Design of tests Tests results Sources of error Future work Portability Base General design improvements Automatic features Accuracy Other uses Evaluation Summary Acknowledgments Bibliography PHOTOGRAPHIC DEVICE FOR ACCURATELY MEASURING FISH INTRODUCTION The photographic measuring device described in this paper was developed to aid the work of the International North Pacific Fish- eries Commission. One of the objectives of the Commission is to devise a suitable method of identifying the various races of Pacific sal- mon so that North American stocks can be differentiated from the Asian stocks. Work to date has shown generally that the differences between the races of salmon are extremely slight. For this reason and others closely re- lated, many aspects of the body characteristics of salmon are being investigated. Among these investigations are bone studies, blood studies, parasite studies, and morphological studies, since one or a combination of these may provide the data needed to characterize the various races (International North Pacific Fisheries Commission, 1955). In the morphological studies, consider- able work is being done on the determination of body proportions and measurements. The taking of accurate measurements, however, from a three-dimensional object such as a fish is difficult. In addition, methods now in use have an indeterminate error due to bias of op- erators. The problem at hand was to develop a method of taking these measurements by means of photography. The advantages of photography over present methods of measurement are: 1 . Tlie pictures of the fish would form per- manent records from which measurements could be checked and rechecked. 2. When fish were needed for measurements that were not contemplated in an original study, these measurements could be taken by the biolo- gist from the many pictures of the fish that would have accumulated over the years instead of his having to wait till the season arrived and then obtaining measurements from only one year's sample. 3. In interpretation of visual characteristics, such as net marks and scale counts, pictures could be analyzed in the laboratory by experts in such analyses. 4. Photography and its associated tools would lend themselves readily to automation, thus tending to minimize human errors and bias of operators . Because of the potential value of a photo- graphic measuring machine and the need it would fill, the development of such a machine was undertaken. Many factors had to be considered in order to develop a machine that would be use- ful to U. S. Fish and Wildlife Service field personnel under the variety of conditions under which they must work. Some personnel work on board motor vessels on the high seas, where storms frequently cause an unstable footing for a measuring machine. Others work in canneries, where lighting conditions may make the use of photography difficult. Still others work on spawn- ing grounds, where portability is important, since the base camp may be some distance from the spawning sites. Yet, despite these difficulties, there must be no sacrifice in the accuracy of the measurements . The objective of this investigation, tliere- fore, was to design a machine that would meet the following qualifications: 1. Give measurements accurate to within + 0.05 cm. 2 . Be fully portable . 3. Incorporate as many automatic features as is possible. 4. Be capable of rapid use in the field. 5. Be rugged. 6. Be not overly expensive . 1 THEORY Since a fish is three-dimensional, all of the points on the fish do not lie in the same plane. Consequently, distances between points on the fish are difficult to measure acurately. Although many types of measurements of dis- tance can be made, the present study is limited to longitudinal measurements (fig. 1), as they are the main type now being made by the U.S. Fish and Wildlife Service in the research work for the Commission. Referring to figure 1, a longitudinal measurement between any two points (Pj and P2) on a fish (or any other tliree-dimensional object) is the distance between the points when they are projected perpendicularly upon the axis of the fish (or object). Since this axis is not access- ible, the measurements are made instead between their perpendicular projections {Q[ and Qo) upon an orientation line (HJ), which is located parallel to the axis. I— LD ■i .1 Ic "^=:7 LD = Longitudinal distonce between ttie points P, and P2 on the fish HJ = Onentotion line poroliel to oxis of fish 0 = Reference point on line HJ Plgur« l.^-HIuatntloa of ■Bsnlog of "lAn^tudliial dlitance". The loo^tudloal dlit«oce b«tv««o the point! F^ and P^ oo the flBh Is eiiual to ^2 ~ ^ OD the orleotetloD line HJ. Photography offers a ready means of projecting P^ and P2 upon the orientation line to obtain the points Q^ and Q9. The distance Q.Q2, however, cannot be measured directly. Instead, each point on the line is located in terms of its distance from some reference point, say 0, on the line HJ; that is, the location of the perpendicular projection of P^ on the orientation line HJ is OQ, . and the location of the perpendicular projection of P„ is OQTT Then OQ^ = OQ^ - Q^Q2 - LD. In locating the perpendicular projection of some point in space, say P^, upon the orienta- tion line by photography, we find there are two sources of error: (1) parallax and (2) perspective. Parallax Error An example of parallax is shown in figure 2. In this figure, point P, which can be any point on die fish, is shown in three different positions above the line HJ. In each case, Oi. Q„, or Qo represents the location of the per- pendicular projection of P upon this line. In only the first case, where P is directly beneath the camera, will Q appear to coincide with P as viewed by the camera. In the other cases, points P„ and P3 will appear to be located at P^ and Po, as illustrated. The distancesP 9Q2 and P oQo are the piarallax errors. The problem of parallax can be solved by the use of two cameras. To show how this can be done, we have two considerations: (1) the special case of determining OQ (fig. 3) where P is located in the plane HABJ formed by two cameras and an orientation line, and (2) the general case of determining OQ (fig. 4) where P does not lie in the same plane with the orienta- tion line but is still in the field of view of the two cameras . Posit ion Position PorollOK Error Porollox Error No Parollan Error Figure 2."EUBpleB of what Is aeant by parallsx error. Special case In the special case (fig. 3) the following definitions should be noted: 1 . Point A is the optical center of the lens of a first camera . 2. Point B is the optical center of the lens of a second camera . 3. Line AB is parallel to the line HJ. 4. Point O is the reference point from which all measurements of distance on the line HJ will be taken. 5. Point P is a point on the fish. 6. Point P lies in the plane HABJ, sub- ject only to the simplifying restriction that OF is positive (that F lies to the right of O) . In a picture taken by camera B, point P will appear to be at point F on line HJ. Similar- ly, in the picture taken by camera A, point P will appear to be at point G on line HJ. Also, we have made D the perpendicular projection of A on the line HJ. Tlie problem now is to derive an equation in which we can use the distances OF and OG to obtain the unknown distance OQ. From the fact that figure 3 contains a number of similar triangles, our required equation is easily derived geometrically as follows: Since triangles ABP and PFG (fig. 3) are similar, then PC = (FG)(PT). (1) but, so, PC = (FG)(PT). AB PT = AD - PO, (2) PQ = (FG)(AD-PQ) (3) AB simplifying PQ = (FG)(AD) (4) FG+AB Consider now the similar triangles AEXj Then or. QG = OG - OP PO AD (5) QG = PQ (OG - OD) (6) ( AD ) now, QG = OG - OQ, (7) and substituting (4) and (7) into (6) we have OG - OQ = ( (FG)(AD) ) (OG - 0D)(8) ( FG + AB) ( AD ) Then OQ = OG - ( (FG)(AD) ) ( OG-OD) (9) ( FG-I-AB ) ( AD ; This reduces to OQ = OG (AB + OD) - (OD) (OF) AB-l-(OG - OF) (10) which locates the perpendicular projection of P on the orientation line HJ. F Q C G andPQG. The distances AB and OD are constants determined by the positions of the cameras in relation to point O on line HJ and to each other. The distances OF and OG are variables deter- mined by the position of P in the plane HABJ. The value OF can be determined from a photo- graph taken by camera B, and that of OG from one taken by camera A. General case In the general case (fig. 4), where we wish to determine OQ when P lies anywhere in three-dimensional space in view of the two cameras, the following definitions should be noted: 1. In this three-dimensional drawing, line HJ lies on the line formed by the intersec- tion of the perpendicular planes 1 and 2. 2. Line OO' lies in plane 2 and is per- pendicular to line HJ. 3 . Line AB lies on the line formed by the intersection of planes 1 and 1' . 4. Plane 1 in figure 4 is the same as the plane HABJ in figure 3, except that lines AD and BC have been omitted to simplify the drawing. 5. Plane 1' is in the position plane 1 would occupy if, using the line AB as an axis, plane 1 were rotated through some angle, say alpha d(_ (subject to the obvious restriction that point P' will lie in the field of view of the two cameras) . 6. Point P' is the position that point P would occupy if plane 1 were rotated through the angle alpha, and point Q, therefore, is the location of the perpendicular projection of the points P and P' upon line HJ. 7. Point F' is the position that point F would occupy if the line FP were extended as plane 1 rotates through the angle alpha; points G' and H' bear similar relationships to points G and H. From a consideration of figures 3 and 4, we see that the derivation of equation 10, al- ready given, applies to the special case where the angle alpha is equal to zero. Since P is any point in plane 1, the prob- lem of locating P anywhere in space (anywhere on the fish) now becomes the simple one of show- ing that equation 10 applies for all values of alpha . This proof depends upon the fact that changing the value of alpha does not change any of the angular relationships in plane 1; for ex- ample, although triangle P'F'G' is larger than triangle PFG for all values of alpha different from 0°, the corresponding angles in these two triangles are identical in size . Similarly, all the other angles in the triangles employed in de- termining equation 10 also remain constant in size as the angle alpha varies . Therefore, since the derivation of equation 10 depends upon the similarity of the triangles and not upon the size of them, this equation holds for any value of alpha; in short, for any location of P in three-dimension- al space. From equation 10, we therefore easily obtain O'Q' . From figure 4, it is apparent that O'Q', is equal to OQ, the location of the perpen- dicular projection of P' on line HJ. A 1 /A T 9 / ^A \ < 0. A i H V 6^^ FOG J \ M'PLME t H \ \ rolAt Usfc la ■ayvbin ibovt plan* 2 and U*I to iB Figure J.— An exampl* ot ttte error caused tj p«rapeciWe; In this picture, the site of the ulaon la sr««ter tban that of the flabln^ veasel because tbe aalann waa cloaer to tbe caBera vban tbe picture waa taken. The perpendicular projection of any other point in space can be located similarly on the orientation line HJ to give some other value say OQ,, . The algebraic subtraction of OQ, from OO2 then will give the longitudinal distance between the two points Q, and Q2- Perspective error The problem of eliminating perspective error is solved by drawing a number of equally spaced, parallel lines (called grid lines) on the base plane. Figure 7 (I) shows such a plane with grid lines 1.5 centimeters apart. Two ob- jects, A and B, of equal length have been placed on this plane, and a camera has been positioned to take a picture of them . The term "perspective", as used here, is defined as "natural objects as they appear to the eye represented on a plane, such as a pic- ture" . Figure 5 illustrates the error caused by perspective; that is, the jumping salmon appears lar^^f^r than does the fishing vessel since the salmon was much closer to the cam- era than was the vessel when the picture was taken. Similarly, if two objects of the same size, such as objects A and B (fig. 6), are placed on a flat board or base plane in such a manner that one is at a greater distance from the camera than is the other, they will not ap- pear to be the same size in a picture taken of them . In the preceding section, we developed equation 10 for eliminating parallax error. This equation was based upon the stipulation that the various projections involved would be free from all other errors. We now see that owing to perspective, this stipulation is not met and that a suitable correction will have to be made for the perspective error as well. To the camera, all objects appear to be lying in one plane regardless of the actual posi- tion of them in space. Hence, for simplicity in the following discussion, we will assume that all of the objects are lying on one plane --the base plane- -since that is the one on which they will appear to lie in the photograph. ,^^ The diagram of the resulting photograph shown in figure 7 (II) illustrates that the grid lines appear to become progressively closer to- gether. Similarly, object A appears to be larger than object B, since object A was closer to the camera than object B was. From our knowledge however, that the distance between the grid lines is actually 1 .5 centimeters, we can deter- mine that both objects A and B are 3.0 centimeters long despite the perspective error. If one end of the object falls between two of the grid lines, as illustrated in figure 8, we must determine the proportionality factor for the distance between the particular lines involved and apply this factor to the measurement of the object in the picture. If, for example, the actual distance between lines 4 and 5 in figure 8 was 1 .5 centimeters and the measurement between them, in the picture, was 0.5 centimeters, then the proportionality factor would be 1.5 = 3.0. Now, if the measurement of A, in the picture was 0.27 centimeters, its actual length would be 0.27 X 3.0 = 0.81 centimeters. Comeip Ovan t* pealtln to tata plettm it abj«-u of t^wl (tw, « ■ad B, «Ueli 11* upOD • board or plao* olUi •4uiiJ.:r 'pacad grid llOM. ^n \ B ^ ,, A ^ Z S 4 5 6 • tvo atj*«ta -ninatntlB ■harla« (1) ba> pan^Ktln ai of ttaa ttm actial (It* to mnmmi to ba of iltterwa\ itM ID • SttoUa^apa 100 (2) hof Ua UH oT «ld tia** aad • knovladga s vas Um otrrUta* Uil* •mr. A ^ 2 3 4 5 2 3 4 5 Flffure 8. "Picture of an object vltb one end Ijlng b«tv»en grid lliMt. Figure 9-— Picture of ■□ object irtth both ends lying betveen grid llnas. To obtain the length of any other object, say C in figure 9, we determine the length of G lying between grid lines 4 and 5 and between grid lines 2 and 3 by the technique used in de- termining the length of A in figure 8. The length of C lying between grid lines 3 and 4 is determined by inspection . The total length of C then is equal to the sum of the lengths lying between grid lines 2 and 3, 3 and 4, and 4 and 5. The length, therefore, of any object lying (perpendicular to the grid lines) anywhere on the base plane (or appearing to lie on the base plane so viewed in a photograph) can be deter- mined free from the error caused by perspec- tive. Thus, if the foregoing techniques are used to eliminate errors due to parallax and to perspective, theory indicates that longitudinal measurements of fish can be made accurately by means of photography. DESCRIPTION OF DEVICE V Since the design of the photographic measuring device may be altered as further tests dictate, only a general description is given here. features, and (5) the wiring. All similar parts are numbered so that the machine can be as- sembled the same way each time . Base and framework The "base and framework" (figs. 10 and 11) consists of four sub-assemblies: (1) the base, (2) the legs, (3) the cap, and (4) the cross members #1 and #2. Base. --The 20" X 48" base was made of a material called "sandwich board", consisting of two, tliin sheets of aluminum between which is a core of honeycombed metal. This type of material was chosen because it combines great flexural strength (i.e., resistance to bending) with light weight. The base was spray -painted with a yel- low, metal-etching zinc chromate primer. Parallel grid lines 1.5 centimeters apart and an orientation line perpendicular to the grid lines were then scribed on the base, deep enough to score the metal. TTie grid lines were then filled with black Indi^ ink, and each was numbered according to the total distance in centimeters between it and the zero line . Photographic Measuring Device The photographic measuring device con- sists of five major units: (1) the base and the framework, (2) the strobe light and power pack, (3) the camera assembly, (4) the automatic Legs. --The legs are hollow aluminum tubes with an outside diameter of .628 inches, 1/ The commercial components described in this paper were chosen only on the basis of local availability. There may be many other types that will serve as well. and a length of 4 feet 5 inches. Each leg has an attached aluminum block that supports the cross members. One end of each of the legs is flattened to fit between two, right-angled bars of aluminum on each corner of the base (figs. 10 and 11). Figure 10.--A3Ben4>led device readj- for opeivtioE Figure ll.--E«plodetJ viev of pbOlOdrapClc Beaiurlng device. {IJ Rubber •tope tb*t keep croea aenber ^1 Tirmly •eaCed tn ti.e elota fan anown In Fl^^urea 12 end 13)i (2) aolenolda; (3) caaeraa; (li) ^ap an] nlna that hold leF:a flraly aeated In tba recepteclea of the cap: (5) croaa Benber fl; (6) edjtiataent waabera tbet afforda adjustment of tbe endvlae rotation of the caaeraai (7) butler end buzter battery; (8) etrobe Ught; (9) refleetor; (10) crose neaber gs vltb adjuatnent bolt that afforda adjuat. ■ant of the eldevaye rotation of tbe eeaerea; (11) bettery boa; (12) avltcb; (13) flaab supply; (lit) 6-volt batteries; (15) aiglial-reglater; (16) lege; (17) bolte used to ettacb lege to baee, (18) Use. Cap. --The cap is composed of four short lengths of aluminum tubing having an inside diameter equal to the outside diameter of the legs. These short lengths are welded together at appropriate angles and serve as sockets for the four legs . Short pins are used to keep the legs seated firmly in these sockets. Cross members #1 and #2 . --Cross members #1 and #2 are round aluminum tubes of the same diameter as the legs. Figures 12 and 13 shows how cross member #1 is attached to the legs. Cross member #1 is 23 inches long and #2 is 8 inches long. Both members together act as stiffeners for the legs and provide a means of attaching the strobe light between the two cameras . The cameras are supported by cross member #1, and the cameras can be aimed at any point on the grid by rotating them sideways and endwise, as shown in figures 14 and 15. Square bars on either end of this cross member provide flat surfaces against which the cameras are held by single bolts . Thus, each camera can be rotated endwise with the bolt acting as the axis of rotation. An "adjustment washer" affords a means of fixing the cameras at any position in the endwise rotation. The flat bar attached at right angles to cross member #1 and extending across to cross member #2 can be raised or lowered by an adjustment screw at cross member #2, thus rotating the cameras sideways (fig. 15). 1 nember fl being attached to figure 13.--Plctur« showlre cross raember ^1 Bfter it is attached to fr^seucri:. Kote i-oimd, hard rubber stops that teep the CTQSB iceaber flnaly se&ted In the slotc, and the short pins that do not allow the cross nenber to slide back and forth, hut do ellcw the cross memher to rotate. Figure llt.-'A double- e3q» sure lUuGtrntlm; the sideways rotctlon of caneras. Strobe Light and Power Pack The strobe light or speed flash used is the "Sunlite 11" model manufactured by the Her shey Manufacturing Co., Chicago, Illinois. The reflector made for this model caused a "hot spot" or area of too much light in the pictures, since it was designed to be used at a greater distance from the subject. Consequently, a flat reflector of our own design was substituted, and this reflector proved to be more satisfactory. Tlie strobe or speed flash power pack is a part of the "Sunlite II" model. Two 6 -volt batteries provide the electrical power to oper- ate the digital-register and the solenoids that trigger the shutters of the two cameras. Camera Assembly The camera assembly consists of two "Exakta" cameras equipped with split-image, eye-level viewfinders and f 2.5, 35 millimeter Figure 15. — A double -expo sure sho'^lnc the endwise rotation of the Angeneiux lenses and the film. The "Exakta" is a single lens reflex type camera. The reflex principal allows the oper- ator to see, in a mirror behind the lens, an image of the scene to be photographed. The lever wind feature of the "Exakta" is another valuable time saver. The film used for these tests was Panatomic-X. Automatic Features There are four automatic features: (1) The solenoids, (2) the buzzer, (3) the digital - register, and (4) the modified switch. Solenoids. --The solenoids are necessary to trip the camera shutters simultaneously. The type used was manufactured by the Heiland Corporation, Denver, Colorado. Buzzer.- -A buzzer was incorporated in the device to warn the operator when one or both cameras were not wound. A common buz- zer, operated from a 4-1/2-volt batter was used. Tlie battery and the buzzer were strapped to tlie strobe light assembly. Digital -register . - -An electrically oper- ated digital -register was placed on the base to' number each picture and each fish consecutively so that the left and right pictures could be matched when the films were read. The digital- register used was a Mercury model manufactur- ed by the Production Instrument Co., Chicago, Illinois. Modified switch. --A modified lever switch was used to trip the solenoids and the digital-register in that order. That is, two con- tacts were made, one preceeding the other, each time the switch was thrown. In this way, the number on the register was recorded in the picture just before the number changed. Wiring The wiring system consists of four cir- cuits: (1) The strobe light circuit, (2) the solenoid circuit, (3) the buzzer circuit, and (4) the digital -register circuit. Figure 16 is a block diagram of these circuits. POWER PACK ncur« 16 .— aiock dlMgnm of vlrlng tjitw. The strobe light circuit is connected to the X side of the two cameras . Note that one part of this circuit is the "metal frame" --the device itself. When the shutters of both of the cameras are not cocked, the circuit is closed or continuous because the X contacts in the shutters are grounded through the bodies of the cameras to the metal frame. When the shutters are cocked, however, tlie circuit is open, or not continuous, because the X contacts are no longer grounded to the "metal frame". If the shutters of both cameras have been cocked, the strobe light can flash only after both shutters have been released or tripped by the solenoids which react almost simultaneously. The shutters were set to remain open 1/25 of a second after the circuit was closed to assure that both shutters were still open when the strobe light flashed. Now if one camera were to remain un- cocked, the strobe light and the camera with the cocked shutter would still operate. In other words, the operator could forget to wind one camera and the mistake would go unnoticed. Because of this the warning buzzer was installed so that when one or both of the cameras were un- wound, the buzzer would sound. One side of the buzzer circuit is connected to the M synch of the two cameras, and the other side is grounded to the"metal frame" . The circuit is completed whenever either shutter is not cocked. The solenoid circuit is closed when the first contact is made in the modified switch. The digital-register circuit is closed when the «»''ond contact is made. The time delay between making of the two contacts allows the picture le taken before the register is advanced. The tch used is #3004, manufactured by Switch - ft Incorporated, Chicago, Illinois. TECHNIQUE OF USE Determining longitudinal distances be- en two points consists of three major steps: Taking the pictures, (2) reading the filn\ and calculating the longitudinal distances . Taking the Pictures Taking the pictures consists of three 3S: (1) Assembling the device, (2) loading adjusting the cameras and connecting the wire, and (3) aligning the subject parallel with the orientation line and taking the picture . Reading Film A microscope with a calibrated stage was used in the normal fashion to determine the film measurements. Two glass plates served to hold the film flat . The measurements were repeated five times and any measurements obviously in dis- agreement with the average were not used. Calculating Longitudinal Distances The calculation of longitudinal distances consists of three steps: (1) From the left and right pictures, determine OQ', the distance from the O line to the perpendicular projection of the first point, say P' . (2) From the left and right pictures, determine OQ" , the distance from the O line to the perpendicular projection of the second point of measurement, say P" . (3) Sub- tract the lesser distance from the greater dis- tance to determine Q'Q" . Calculation of OQ' OQ' is calculated from equation 10 (see "Theory"). The use of this equation requires the determination of the distances AB, OD, OF, and OG and the insertion of these values in equation 10. Etetermination of AB. --The distance AB is a constant. It is the distance between the optical centers of the two cameras (as in fig. 3) . The distance between the points on the outside of the lenses, which roughly correspond to the op- tical centers of the lenses, was measured with a steel tape. This distance was used for the value AB. Determination of OP. --The distance OD is a constant. It is the distance from the O or reference line to the perpendicular projection of the optical center of camera A, point D, (as in fig. 3) upon the base plane. The base plane or grid of the photographic measuring device was leveled. A point, judged to be opposite the op- tical center of the lens, was chosen on the out- side of the lens barrel, and a plumb bob was suspended from this point. The distance OD was then measured with a steel tape. Determination of OF . - -The determina- tion of OF consists of four steps. (1) From the left film, determine the proportionality factor for the distance between the two grid lines that lie on either side of the first point of measure- ment (F). (2) Measure the distance from the first point to the nearest line lying to the left of this point (assuming that O line lies to the left also). (3) Multiply this distance times the pro- portionality factor. (4) Add the distance from the O to the left line to the results of (3) to ob- tain the total distance from O to F /the position of point P' (the first point) as it appears in the right picture/. Since the distance from the O line to any other line is equal to the number of that line, then this distance can be read directly. Determination of OG . - -The procedure for the determination of OG is the same as that for the determination of OF except the left film is used instead of the right film . Substitution of AB, OD, OF, and OG into equation . - -To obtain OQ', now substitute the con- stants AB and OD, and the variables OF and OG 10, / OQ' = OG (AB + ob) - (OD) (OF)7 AB + (OG - OF) into equation Calculation of OQ" Since AB and OD are constants, we need only determine the distances OF and OG from the right and left film respectively (as explained under "calculation of OQ' ") and then substitute these values into equation 10. Calculation of Q'Q" We have now determined the two dis- tances OQ' and OQ" . If OQ" is larger than OQ', then 0Q"_^ OQ'^Q'Q", the longitudinal distance between Q' and Q" . And, since Q' and Q" are the perpendicular projections of the points P' and P", the distance Q'Q" is also the longitudinal distance p.p.. PERFORMANCE The performance of the machine can be considered from the following four categories: 10 portability, automatic features, efficiency, and accuracy. Portability The base of the photographic measuring device used in the tests was not designed to be disassembled. Consequently, the device cannot be considered fully portable . Since making the base in more than one part may introduce fur- ther errors, it was decided to test the device in its present form first to have a basis of com- parison for any modifications made later. Automatic Features Since the device has not been operated without the automatic features, there is no way of deterinining the degree of added efficiency for which they are responsible. In general, these features were added to accomplish two . things: (1) To save time when fish are being measured in the field and (2) to eliminate pos- sible sources of mistakes on the part of the operator. From our experience in using the machine, we feel that all of these features are valuable aids in these two respects. Efficiency Taking Measurements The efficiency of the device under field conditions remains to be tested. However, it can be operated in the field or under laboratory conditions at a greater speed than the methods now in use. Under certain conditions in the field, a greater speed of operation will mean a larger sample of fish measured. In canneries especially, where small boatloads qf fish are processed immediately after they are received, time becomes invaluable; Reading Film and Calculating Longitudinal Distances Reading the film with the microscope and calculating the longitudinal distances with these readings is tiring and time consuming. The fact that this must be done at all is a disadvantage unique to this photographic method. In methods now used by the Fish and Wildlife Service, the measurements are read directly from the measur- ing device or from a paper tape upon which the measurements have been stamped or recorded by the device . In the photographic method, four film measurements that have been corrected for perspective are needed to calculate each longitudinal distance. Accuracy Design of Tests The primary objective of these tests was to determine the accuracy of the device in its present form. At the inception of this work, we decided that a tolerance of -I- 0.05 centimeters would be our goal . A solid aluminum bar was used as the subject instead of a fish, since a subject of in- variable length was necessary so that a com- parison of the computed length to the actual length could be made . Since tlie length of the subject and the position of the subject on the base may have some effect on the accuracy of the results, tests were made using subjects of different lengths placed at different points on the grid. A bar 25.20 centimeters long was placed in nine posi- tions on the grid for each of three tests - Aj, A2, and An. Figure 17 shows the general loca- tion of eacn of these positions. Similarly, a bar 76.11 centimeters long was placed in six positions on the grid in test B; two positions above the orientation line, two positions on the orientation line, and two positions below the orientation line. Since the constants used in formula 10 depend upon the positions of the cameras, it fol- lows that the positions of the cameras should always be the same after the device is assembled. This was tested by disassembling and assembling the device prior to each of the three tests - A,, A , and A„ ^2 3- Tests A, , A,, and Ao, therefore, con- sisted of 9 negatives from the left camera and 9 negatives from the right camera; one left and one right negative for each position. Test B con- sisted of 6 left and 6 right negative." , 11 Test Results The negatives for test B were read only once because of the short time available . Sim - ilarly, the negatives for positions 1, 2, 3, 7, 8 and 9 of test A. were read only once. The re- sults are listed in table 1. Figure lT>»niust ration abovlDg general locetton of poeltlono ^1 throu^ #9 a baoe for testo Ai , A2, and A3.. Meat of the Tcrtlcel grid llneo have been ooltted to elmplify the stetcb. The negatives of positions 4, 5 and 6 (the positions of the bar on the orientation line of tests A , A , and A ) were read 5 times by a first reader. The same negatives of test A. and A were read three times and those of test A,, 2 •^ read twice by a second reader. Tlie results are listed in table 2 . Table 1 shows that in test A, the range of the errors for all positions was from -0.01 to +0.04 centimeters. In test B the range of the errors for all positions was from -0.03 to -t-0.04 centimeters. These results indicate that the error for a subject of any length lying anywhere on the grid will not be radically different from a subject of any other length lying anywhere along the orientation line. The range of all the errors shown in table 2 is from -0.05 to -1-0.05 centimeters in- dicating that the positions of the two cameras do not change enough from one assembly to the next to cause an error that greatly exceeds the toler- ance limits of -1-0.05 centimeters. The range of errors for Reader No. 1 is -0.05 to -K).05 centi- meters while the range of errors for Reader No . 2 is -0.02 to +0.05 centimeters. In general, the errors obtained by Reader No . 2 were well on the positive side, since only 2 of the 24 readings POSITION ABOVE ORIENTATION LINE POSITION ON ORIENTATION LINE POSITION BELOW ORIENTATION LINE TEST POsmoN NUMBER 1 Z 3 4 5 6 7 8 9 A, LeocU 85 .» 85 JO 25^ 25.21 25.22 75.23 25.19 25.21 25.22 Actual 2S.20 2$.30 25.20 25 .» 25 JW 25^ 25.20 25.20 25.20 Error «C.lA 0.00 tO.Ol *0.01 ♦O.QB «0.03 -O.Ql *0.01 *0.(B B POSITION NUMBER ' 2 3 4 5 6 CalcuUtad 76.13 76.06 76.15 76.09 76.09 76.U LHWU 76. U T6.U 76.U T6.U T6.U 76.U Error *o.oe -0.03 *O.0>. -O.OB -0.02 0.00 TsUa 1.— IMMlt* or t«*t Aj ■ 1 iMt fi. All *mli»* K READER NUMBER 1 READER NUMBER 2 TEST POSITION READINGS READINGS -". ■ 2_[ 3 1 2 ; 3 1 4 1 5 ^ 4 £5.18 25.19 I ^5-lfl 1 25.19 1 25.18 .(-o.oe) (-o.ca), (-o.oe)l (-0.01}: t-o.QS) 25.21 25-25 ' 25-23 (..0.01) (*0.05) (•0.03) 5 a5.21 25.19 i 25.18 25.1B ' 25-15 iM.ca.) (-0.01) (-O.CE} (-o.oe) (-0.05) 25.22 25.23 25.23 («o.ce) (♦0.03) {.0.03) 25.23 25.25 25.25 (*0.C3} (.^.05) (*0.05) 25-19 25-2'' 35-2h (-0.01) (fO.Oit) (*C.OA) 25.20 25.2li 25.23 ( 0.00) (rf.Olt) (*0.03) 25.1a 25.25 25.2fc (-o.oe) (*o.o5); (•o.ofc) 6 25.22 a5.2"t 35.23 25-22 25.21 («o.ce) (4O.CA) (^.03) (*O.CQ) (*0.Q1) flj 4 25.19 25-21 25-30 25-30 25-19 (-0.01) (to.oi) (*o.oo) (to.ooj (-O.ca) 5 25.21 25. a 25-21 35-Sl 25-21 (♦0.01) (*c.oi) (.0.01) (rf.Ol) (*O.01) 6 Z5.2* 25.2h 25.2'' 25-23 , 25-25 (+O.0U) (♦O.Ofc) (♦O.Ofc) (*0.03)l (tCOS) *3 4 '25.17 25-20 25.18 25-19 25.19 (-0.03) ( 0.00) (-O.OG) (-0.01) (-0.01) 25.23 25.22 (4O.O3) (rt-OB) 5 25.22 25. Id 25.20 25. IB 25.19 (♦O.CG), (-0.02) (0.00) (-0.02) (-O.Q1) 25-2>t 25.2^ l*C. 3 : 5 MBL WHOI Library - Serials 5 WHSE 0 163