m/min. At a preset depth, the ballast was released 

 and the system returned to the surface. 



Fish lengths were measured from photographic 

 enlargements with an x-y coordinate reader and 

 only those fish enclosed by a circle of 6 to 10 cm in 

 diameter, drawn centered on the photograph, were 

 counted in order to reduce computer processing 

 time and peripheral photographic distortion. 

 Repeated measurements of a photograph indi- 

 cated a mean error in individual body length of 

 3.49r and a maximum error of less than 9.0% for 

 any individual. 



To estimate the distances from the camera to the 

 fish it was assumed that all the fish were of the 

 same size, were all oriented perpendicularly to the 

 camera lens, and thus the differences in fish image 

 size were dependent only on the distance from the 

 camera. The distance between any fish and the 

 camera was determined by calculating the ratio of 

 the standard fish size to the 35-mm negative 

 image size and substituting this value into the 

 underwater calibration equation of the camera 

 (Figure 2). The mean standard length of 12. cm (s 

 = 1.9 cm) for anchovy in southern California 

 waters (Mais 1974) was used as the standard fish 

 size. 





UJ 



< 



< 



E 

 E 

 m 

 ro 





O 



< 



UJ 



or 



10 20 30 40 



DISTANCE FROM THE CAMERA (m) 



FIGURE 2. — The calibration curve for the Isaacs-Brown free 

 vehicle drop camera. This camera system was calibrated under 

 water by photographing objects of known sizes at fixed distances 

 and the ratio of the real object to negative image size (y) was 

 plotted against distance from the camera ix). The equation for 

 the line is.v = 19.56*. The distance to a fish was then determined 

 by calculating the ratio of the standard fish size (12 cm) to the 

 35-mm negative image size of that fish. 



A computer program calculated the lengths of 

 the fish and produced a cumulative percent dis- 

 tribution of their sizes. One would expect the 

 number offish with small image sizes to increase 

 with distance from the camera lens, but analysis 

 revealed that a distance existed in most photo- 

 graphs at which the numbers of smaller fish failed 

 to increase presumably because the more distant 

 fish were not resolved owing to overlap, water 

 clarity, and loss of lighting. An arbitrary limit was 

 established at that image size by noting a change 

 in slope on the graph of the cumulative percent 

 distribution offish lengths (Figure 3) and all fish 

 smaller than the limit were not considered. 



After establishing the minimum fish image size 

 to be included in the program, a three-dimensional 

 model of the photograph was constructed by 

 calculating a third coordinate, z, based on fish 

 image size and by adjusting thex and y coordinates 

 for distance from the camera. The midpoint of each 

 fish was then determined and a mean distance to 

 the nearest neighbor was calculated by compari- 

 son with the midpoints of all the fish. The density 

 of the school was computed by dividing the num- 



B 



LIMIT 



40 30 20 10 



F ISH LENGTH (digitizer units) 



FIGURE 3. — The cumulative percent of length frequencies (in 

 arbitrary units) for the fish measured in photograph 10 (Figure 

 4). Graphs of this form were made for each photograph analyzed 

 in order to determine the distance beyond which all fish images 

 were not resolved. The limit was made arbitrarily at the first 

 apparent decrease in slope of the distribution. 



231 



