Experiments with scanner: relative motion MUSE Workshop
WCPE Istanbul, July 1-6, 2012
Published by the MUSE group (More Understanding with Simple Experiments) , Physics Education Division (PED) of the European Physical Society (EPS) http://education.epsdivisions.org/muse/
Experiments with scanner: relative linear motion[1],[2]
WORKSHEET
Introduction
Optical scanner is computer operated device for taking images of paper documents. Scanner can be used also for taking images of other objects, providing they are not larger than the scanner window and that they are placed close to it.
The principle of operation is rather simple. Stepper motor is moving the scanner head with a constant velocity along the document. During this time the optical system in the scanner head is projecting a narrow strip of the document on the light sensitive detector. Signals from the detector are sent to computer and stored as a time sequence of line images. Information about positions in direction perpendicular to the scanning direction (let’s call it y direction) are already included in line images but positions in the scanning direction (x coordinate) depend on the head motion and therefore had to be determined in some way. For our purpose we will use the following simple explanation. The computer measures time of occurrence of line image and then converts time intervals into distances in scanning direction by “knowing” that the scanner head was moving with constant speed vs
.
Let’s illustrate this with a simple one dimensional example. Imagine you place a stripe that consists of black and white segments on the scanner and align it with the scanning direction as shown in figure below.
While the scanner head (here represented by the narrow gray rectangle) is moving with constant speed of 10 cm/s to the right, the computer records light intensity (bright or dark in this case) and corresponding times when these measurements were obtained. The recorded data for this particular case are shown in table below.
t(s) / 0 / 0.1 / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8 / 0.9 / 1.0B
It was assumed that at time t=0 the scanner head was at the position x=0. As expected the pattern in the bottom row of the table resembles the original object but note that the correct dimensions of the object can only be deduced from the measurements if the speed of the scanner head is known.
In the activities that follow we will use the computer scanner and a toy car. We will fix a transparency with parallel lines on the scanner window to set the scale. Distance between adjacent lines is 1 cm.
PROBLEM A
The following scanned image has been obtained when a toy car has been placed on the scanner.
The car was motionless during scanning and the scanner head was moving from left to right with constant speed vs (observe movie 1).
We will be using x(t) graphs to study motion of the car and scanner head in various situations. The graph below shows time dependence of the position of the car (horizontal lines) and the scanner head (tilted line), as seen from the lab system. We will choose the origin of the x axis at the very left side of the scanner window, with its positive direction oriented in the direction of scanning (see photo on the previous page).
I. Mark on the graph or explain how to determine from the graph the following quantities:
1. xF – initial position (at time t = 0) of the front of the car
2. xB – initial position (at time t = 0) of the back of the car
3. a – length of the car
4. b – length of the scanned image of the car
5. vs – speed of the scanner head
6. va – speed of the car
7. ta – time needed for the scanner head to scan the car only
PROBLEM B
Car will be placed on the scanner window with front part pointing in the direction of scanning, as in previous case and moved with constant speed during the scanning. The magnitude of the speed of the car will be smaller than the magnitude of the speed of the scanner head (va < vs). The car will be moving in the same direction as the scanner head (to the right). Observe movie 2.
I. Make a prediction how will the scanned image of the car in this case compare with the image shown in problem A. Describe your prediction by drawing a sketch of the anticipated image. Sketch your prediction image under the sketch of the car from problem A, next to letter B. Make sure you draw all details including the letters that are painted on the bottom of the car.
Describe your reasoning in few sentences:
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
II. Wait for the workshop leader to show you the experiment. Carefully observe the scanned image and sketch again how it compares with the image of motionless car from problem A.
III. Does your prediction in question I. agrees with the outcome of the experiment (circle your answer)?
YES NO
If it does not agree, try to describe what part of your reasoning was wrong
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
IV. Draw the x(t) graph for the motion of the car and the scanner head in this problem. You may assume that at t =0 the car and the scanner head were already moving with constant speeds.
I. Mark on the graph or explain how to determine from the graph the following quantities:
1. xF – initial position (at time t = 0) of the front of the car
2. xB – initial position (at time t = 0) of the back of the car
3. a – length of the car
4. b – length of the scanned image of the car
5. vs – speed of the scanner head
6. va – speed of the car
7. ta – time needed for the scanner head to scan the car only
V. Check if characteristics of the image are consistent with the quantities that can be determined from the graph.
PROBLEM C
Based on the scanned image obtained in the last experiment (Problem B) calculate the speed of the car as measured in the laboratory reference frame va and the speed of the car relative to the scanner head vrel (i.e. speed of the car as measured in the reference frame that is moving together with the scanner head). The speed of the scanner head was equal to vs = 7.5 cm/s. Show your calculation and use the same symbols as you did on the graphs.
WAIT FOR SHORT PRESENTATION OF WORKSHOP LEADER.
PLEASE, DON’T TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO.
PROBLEM D
This time the car will be placed on the left edge of the scanner, outside the glass, as shown in the photo on the right. During the scanning the car will be moving with constant speed larger than the speed of the scanner head (va > vs) and in the same direction as the head. Observe movie 3.
I. Using the linear stripe model try to prediction how will the scanned image of the car in this case compare with the image shown in problem A. Describe your prediction by drawing a sketch of the anticipated image. Sketch your prediction image under the sketch of the car from problem A, next to letter B. Make sure you draw all details including the letters that are painted on the bottom of the car.
Describe your reasoning in few sentences:
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
II. Wait for the workshop leader to show you the experiment. Carefully observe the scanned image and sketch again how it compares with the image of motionless car from problem A.
III. Does your prediction in question I. agrees with the outcome of the experiment (circle your answer)?
YES NO
If it does not agree, try to describe what in your reasoning was wrong
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
IV. Draw the x(t) graph for the motion of the car and the scanner head in this problem. You may assume that at t =0 the car and the scanner head were already moving with constant speeds.
I. Mark on the graph or explain how to determine from the graph the following quantities:
1. xF – initial position (at time t = 0) of the front of the car
2. xB – initial position (at time t = 0) of the back of the car
3. a – length of the car
4. b – length of the scanned image of the car
5. vs – speed of the scanner head
6. va – speed of the car
7. ta – time needed for the scanner head to scan the car only
V. Check if characteristics of the image are consistent with the quantities that can be determined from the graph.
1
[1] The MUSE group (G. Planinsic, E. Sassi, L. Viennot) takes responsibility for the content of this paper (July 2012). The intellectual property remains with the author Gorazd Planinšič.
[2] Author wishes to acknowledge Eugenia Etkina and Bor Gregorčič for valuable discussions and suggestions.