A Camera as an Angle-Gauge

1. A Camera as an Angle-Gauge Brock Stewart Chris J. Cieszewski Michal Zasada The University of Georgia

2. Camera • Focal Point: where all rays converge • Focal Length: distance from focal point to center of film • Inverted image formed on film

3. Camera • Focal Point: where all rays converge • Focal Length: distance from focal point to center of film • Inverted image formed on film

4. Angle-Gauge • Angle-Gauges project angles. • Used to project the Critical Angle in Angle-Count Sampling. • Angle-Count Sampling: • Project constant angle, the Critical Angle toward trees • Count trees that appear wider than angle • BA/acre = (# counted)*BAF

5. Angle-Gauge

6. How is a camera used as an angle-gauge? • Take pictures at sample points Focal Point is over the Sample Point Horizontal Field of View represents a partial sweep

7. How is a camera used as an angle-gauge? • Take pictures at sample points • Trees counted in office on pictures Focal Point is over the Sample Point Horizontal Field of View represents a partial sweep

8. How are trees counted on pictures? By comparing their DBH on pictures against a width that represents the Critical Angle.

9. How are trees counted on pictures? The width used to represent the Critical Angle on pictures is called the Critical Width.

10. How are trees counted on pictures? The size of the Critical Width depends on how far it is from the center of the picture.

11. How are trees counted on pictures? CW’s if 4x6 in. picture, BAF=10, f =50mm

12. How are trees counted on pictures? The Critical Width changes across a picture, but not by much. (Critical Width)*3

13. What is the Critical Width?

14. Critical Angle Borderline Tree directly in front of camera • We know that when a tree is borderline, this means that the arms of the Critical Angle are tangent to the tree’s cross-section

15. Critical Angle Critical Angle Borderline Tree directly in front of camera Similarly, the angle between light rays reflecting off either edge of the tree and traveling through the Focal Point to the film is the size of the Critical Angle Same angle on both sides of the Focal Point

16. Critical Angle Critical Angle Borderline Tree directly in front of camera Distance between the two points on the film where the arms of the Critical Angle meet the film is the Critical Width on the film.

17. 4 ½ Feet Borderline Tree directly in front of camera • Image of the tree on the film is borderline

18. Critical Angle Critical Angle Critical Angle Critical Angle CW tree 2 CW tree 1 Why does the critical width change? 1 2

19. (x2,y) (x1,y) 3-D geometry f

20. (x2,y) (x1,y) |x1| |x2| 3-D geometry CW = |x2| - |x1| f

21. Formula for Critical Width on Pictures f = Focal Length α = Critical Angle x, y = picture coordinates scaled down to film coordinates (x,y) = point where Critical Angle is projected

22. Formula for Critical Width on Pictures This gives Critical Width as a width on film The result is scaled up to picture units

23. 3-D geometry TA =θ2 – θ1 (x2,y) (x1,y) θ2 θ1 TA f

24. Formula for Tangent Angle of trees on Pictures f = focal length x, y = picture coordinates scaled down to film coordinates x2 is farthest from y-axis x1 is nearest to y-axis

25. Data

26. Data Average: -2.95% Std. Dev.: 13.66%

27. Why use a Camera as an angle-gauge? • “Oh, that’s what that stand looked like”, plus, can make meaningful measurements on the pictures. • Historical records, repeated measurements, • Borderline trees evaluated in office

28. Summary • Take pictures at sample point • Use the changing “Critical Width” to count trees • Measure Tangent Angle of borderline trees • Need to know: • Camera’s focal length • Film Dimensions • Simple software can be used to count trees with a changing width, also check borderline trees