a camera as an angle-gauge

A Camera as an Angle-Gauge

Brock Stewart

Chris J. Cieszewski

Michal Zasada

The University of Georgia

Camera

Focal Point: where all rays converge

Focal Length: distance from focal point to center of film

Inverted image

formed on film

Angle-Gauge

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

Angle-Gauges project angles.

Angle-Gauge

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

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

How are trees counted on pictures?

By comparing their DBH on pictures against a width that represents the Critical Angle.


The width used to represent the Critical Angle on pictures is called the Critical Width.


The size of the Critical Width depends on how far it is from the center of the picture.

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


The Critical Width changes across a picture, but not by much.

(Critical Width)*3

What is the Critical Width?

Borderline Tree directly in front of camera

Critical

Angle

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


Critical

Angle

Critical

Angle

•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


Critical

Angle

Critical

Angle

•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.


4 ½ Feet

Image of the tree on the film is borderline

Why does the critical width change?

12

Critical

AngleCritical

Angle

Critical

AngleCritical

Angle

CW tree 1CW tree 2

3-D geometry

f

(x2,y)(x1,y)

3-D geometry

f

(x2,y)(x1,y)

CW = |x2| - |x1|

|x2||x1|

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

2arctantan

2arctantanCW

2222

22 yf

x

yf

xyf

Formula for Critical Width on Pictures

2arctantan

2arctantanCW

2222

22 yf

x

yf

xyf

•This gives Critical Width as a width on film

•The result is scaled up to picture units

3-D geometry

(x2,y)(x1,y)

θ1

θ2

fTA

TA =θ2 – θ1

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

2 1

2 2 2 2arctan arctan

x xTA

y f y f

Stand Point Field Picture Diff. % Diff.1 21 21 0 0.02 23 28 5 21.73 19 17 -2 -10.51 22 22 0 0.02 24 21 -3 -12.53 25 28 3 12.01 13 11 -2 -15.42 15 15 0 0.03 13 9 -4 -30.81 10 10 0 0.02 15 16 1 6.73 15 14 -1 -6.7

4 No Difference3 Field < Pics5 Field > Pics

3

4

# Trees "In"

1

2

Average: -2.95%

Std. Dev.: 13.66%

Data

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

SummaryTake pictures at sample pointUse the changing “Critical Width” to count treesMeasure Tangent Angle of borderline treesNeed to know:

Camera’s focal lengthFilm Dimensions

Simple software can be used to count trees with a changing width, also check borderline trees

a camera as an angle-gauge

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