Visual Size: Calculating a Visual Angle

Visual Size: Calculating a Visual Angle

A Psychology 469 (Visual Perception) Tutorial

Created by Donald Kline and Lisa Lynk

Vision and Aging Laboratory

Department of Psychology

University of Calgary

Version 1.2 – Jan. 2001

1. How to Use this Tutorial

Welcome to the PSYC 469 tutorial on Calculating a Visual Angle.

The size of an object’s image on the retinal depends on two things, the actual size of the object, and its distance from the eye. In this tutorial, you will learn how to use object size and object distance to calculate an image’s angular size on the retina. The concept of an images angular size is essential to understanding a variety of visual phenomena including acuity, depth perception, and the contrast sensitivity function (CSF) of the visual system for objects of different size.

These tutorials cover several different topics in vision. Each topic is covered in a separate module, which consist of repeating sequences. On the first page in each sequence, you will receive a brief presentation of information , on the following page you will be asked a question about that information, and on the third page, you’ll see the question along with the correct answer to the question.

To use the tutorials, select the topic from the menu by clicking on it. Study the information pages carefully and subsequently select the ‘next’ button. This will automatically bring you to the question page. After recording your answer, click on ‘answer’ and the correct one will appear. If your answer is not correct, you should review the relevant information by selecting ‘information’. This will take you to the preceding information page. Read the page over again very carefully proceeding to the Question and Answer once you have done so.

You can quit the tutorial anytime by returning to the main Tutorial Menu and selecting ‘tutorial’ button located in the corner

Using The Tutorial

You should read over each information Page very carefully, and then click on ‘next’. Record your answer to the question on the question Page, and then use the “Answer Page” link to see the correct answer. If your answer is correct, use the Information, Question and Answer Page links to proceed onward through the tutorial. Anytime that you answer is not correct, you should use the question Page link on the Answer Page to return to and read the previous Information Page very carefully.

You can quit the tutorial at any time, by returning to the main Visual Perceptual Tutorial menu. Just select the “home” button located in the lower left hand corner of every pate. Once there, you can exit the tutorial series by selecting the quit button.

Information Page: Why Use Visual angle for Size?

In vision research, the size of objects is typically expressed in terms of its seconds (60 seconds = 1 minute). By using this approach, objects of different real-world sizes viewed from various viewing distances can be compared in terms of their true “visual” size on the retinal. This approach also makes it useful for translating size discrimination thresholds into acuity. For example, if a person can detect a minimum gap or feature that is 1 minute across, that corresponds to a visual acuity of 20/20 regardless whether the acuity target (e.g. a letter, grating or Landholt C) is near and smaller, or far away and larger.

Question Page

In vision research, the retinal image size of objects of various actual sizes, viewed from different distances can be compared using the angular unit of a.) ______. Using this unit, someone with 20/20 acuity is able to discriminating a target feature (e.g., the gap in a letter “C”) which is b.) ______in size, regardless of the target’s distance from the observer.

Answer Page

Question: In vision research, the retina image size of objects of various actual sizes, viewed from different distances can be compared using the unit of a.) ______. Using this unit, 20/20 acuity is equivalent to discriminating a target which is b.) ______in size, regardless of its distance from the observer.

a.)  DEGREES

b.)  1 MINUTE

Information Page

The relationship0 between the angular size of the image in otne retinal on one hand, and target size and viewing distance on the other, can be seen below. Although object A is twice the size of object B, it is also viewed from twice as far away (i.e. from distance D versus 0.5D). Thus, the visual angles of object A and object B are identical on the retina (i.e. q).

Question Page

2. As an object is moved closer to the eye its visual angle on the retina will a.)______. Therefore, the visual image size of an object can be specified only if the object’s b.)______from the eye is also known.

Answer Page

2.  As an object is moved closer to the eye its visual angle on the retinal will a.) ______. Therefore, the visual image size of an object can be specified only if the object’s b.)______from the eye is known.

a.)  INCREASE

b.)  DISTANCE

Information Page

If the size of an object and its distance from the eye are both known, its visual angle (theta or q ) can be calculated using trigonometry. To use trigonometry, it is necessary to work with right angles. For larger angles (> 6 degrees) it should be done by using the “exact method” : 1.) multiply the object’s size (i.e. width or height) by 0.5 (i.e. 0.5A), and divide that by the viewing distance (D) in the same units to find the tangent of the angle 0.5q : 0.5A/D = tan (0.5q ).

After finding the angle associated with the tan of 0.5q (i.e. the arc tan), all you need to do is multiply 0.5q by 2 to get q in degrees or fractions of degrees.

Question Page

3. To calculate the visual angle (q) of a feature most accurately you should begin by first calculating the a.) ______of 0.5q , which is equal to b.) ______times the size of the feature divided by its c.) ______.

Answer Page

3. To calculate the visual angle of (q) of a feature most accurately you should begin by first calculating the a.) ______of 0.5q , which is equal to b.) ______times the size of the feature divided by its c.) ______.

a.)  TANGENT

b.)  0.5

c.)  DISTANCE

Information Page

Here’s an example of how the angular size of a 7cm x 7cm, square 6 meters away from the observer’s eye would be calculated.

Tan (0.5q) = (0.5 x 7cm)/(6 x 100cm)

= 3.5/600

= 0.0058

0.5q = tan –1 (0.0058)

= 0.3323 degrees

q = 2 x 0.3323

= 0.665 degrees ( or 0.665 x 60 ) = 39.9 minutes

Question Page

4. Calculate the visual angle size of an 8cm feature at a 100-cm viewing distance using the “exact” method. The tan of 0.5q is equal to a.) ______, which corresponds to an angle of b.) ______degrees. The visual angle of the feature is therefore c.) ______degrees or d.) ______degrees and e.) ______minutes.

Answer Page

4.)

a.) 0.04

b.) 2.29

c.) 4.58

d.) 4

e.) 34.8

Information Page

Small Angle Approximation Method: for smaller objects or features (less than 6 degrees or so), the visual angle can be approximated closely and quickly without first finding 0.5q. Instead, all you do is divide feature size by viewing distance to find tan q, and thus q itself.

tan q = (size of object in cm)/(distance in dm)

q = arctan (size)/(distance)

Question Page

5. Using the “small andgle” approximation method, calculate the visual angle of a 48 cm target feature that is viewed from 6 meters. The tangent of this visual angle is a.) ______and the visual angle is b.) ______degrees.

Answer Page

5.

a.) 0.08

b.) 4.58

Information Page

Compare your answers to question 4 and 5 on the preceding cards. You will see that although you used the “exact” method on question 4, and the “small angle approximation” method on number 5, the visual angle size was virtually the same (about 4.58 degrees) in both cases. Because the angular size of the two targets was small (less that 6 degrees), it didn’t matter if the angle was calculated from tan q or from tan 0.5q.

A Useful “ Rule of Thumb”

To provide a quick check of the general accuracy of your visual angle calculation, you can use the “thumb test”. The width of your thumb held at arms length is approximately 2 degrees of arc. If you simply compare the width of your thumb at arms length to an object or feature, you can make a quick approximation of its visual angle at your eye. For example, if a stimulus is about one-half the width of your themb when viewed from the proper viewing distance, and if your calculation shows that it is about 1.0 degree wide, it is probably correct.

Question Page

6. If you place yourself at the correct viewing distance from an obje t that your calculations have indicated is 60 minutes wide, when you view the object against your thumb at arm’s length it should be approximately a.) ______the width of your thumb.

Answer Page

a.) half