SOFIA

Imagine a rectangular array of sensors about 500 across and 500 high focused on a stars in a portion of the sky only a few arc-minutes wide. (Each degree of angular view is equal to 60 arc-minutes.) The SOFIA observatory will use such an array to measure where the telescope is pointed and send the data back to guide the repositioning of the telescope via torque motors.

In this experiment we will build a two sensor array and measure its ability to detect the angular position (in one direction or dimension) of a lamp which will simulate a star. The telescope must measure angular position of 2 or more stars in two dimensions, and with higher precision, but our 2 sensor array illustrates the same fundamental requirement for one simulated star in one dimension. We need to understand a little about the optics associated with the phototransistors and how phototransistors work. And we will need to build a shield and to add focusing optics to the phototransistors to increase their sensitivity to angular changes in light. Finally we will test the two sensor array to measure its sensitivity to angular position of a light source.

Objectives:

1. Explore the characteristics of a phototransistor.
2. Construct directional sensors from two phototransistors with a simple lens and shields.
3. Integrate the directional sensor signals with Interactive C code to compute the angle discriminating function in real-time.

Phototransistor Characteristics and Requirements

A phototransistor is a light-sensitive device similar to other transistors which act as current amplifiers, except that it converts visible light, or photons, to current which is then amplified. The output current creates a voltage drop which is in reverse proportion to the light intensity until it is reduced to small value. If the phototransistor is plugged into one of the analog input ports on the Handy Board, the voltage can be read as a digital number, ranging from 255 for minimal light to about 10 for bright/close light.
The phototransistors in the Botball kit (Panasonic PN168) will register a value of about 10 for an unfocused pen lamp (~4w) at 30-40 cm. Unfortunately, the optical characteristics of these phototransistors are not well matched to the requirements for our sensors. In order for the two element array to be sensitive to direction, each phototransistor should only respond to light coming from a narrow range of angles, but each of our phototransistors is enclosed in a plastic dome or lens which gives it a wide angular view. This also makes it relatively insensitive to the rays of light coming from a small source like our pen lamp (simulating a star). To correct the problem we will mount the phototransistor in a small box with a narrow opening and fit it with a focusing lens to give it better sensitivity in the direction of the opening. We want the angular response to be about 5 degrees in the direction of the beam movement (up & down) and about 15 degrees in the side-ways direction. These requirements lead to the sizing of the shield box in the construction description. The focusing lens does not have any tight requirements so it can be made from any transparent plastic. The construction description suggests soft plastic bumpers so they can be easily cut to fit the box. The students are encouraged to experiment with other optics and with the placement of the lens in front of the phototransistor if they are interested in improving the sensitivity and directionality of the sensors.

Directional Sensor construction

Materials:
masking tape (1/2 inch strips)
popcicle sticks
3x5 note card stock
black marker pen
clear , soft plastic bumpers, ~ 9 mm diameter x 2 mm high
latex glue
sharp craft knife
Make shields and lens for two phototransistors, for each sensor:
4. cut a popcicle stick down the middle and make four 5 cm lengths.
5. Cut two rectangular pieces 2 x 5 cm each from the card stock.
6. Glue sticks to each other and to one card piece as shown to make a channel:

7. Color the inside of the channel black with the marking pen.
8. Remove bumper from its card and stick to a clear plastic bag (so the sticky side won’t attract dust); cut a 4 mm slice from the middle of a bumper with the knife to make a lens:

side   top

9. Mount the lens and phototransistor in the open channel with the lens about in the middle, 2.5 cm from one end as shown from above (hold with masking tape):

10. Cut a short piece of popcicle stick, about 10 mm, and tape on top of phototransistor wire leads to help hold it in position, and block light from the rear .
11. Blacken the inside of the second piece of card stock and tape on top to complete each sensor.

Array Assembly and Test Procedure

Each phototransistor & shield sensor should be measured to establish its ability to discriminate small changes in angle relative to a lamp. Mount each sensor on the sensor testing jig built in experiment 5, and use the sensor test program sensa&b_cal1.c to gather its data (connect sensor to analog(0) and analog(1) inputs). Be sure to measure the distance of the lamp from the sensor, and set it the same from each sensor.

1. The lamp and sensor configuration provides us with an opportunity to verify a fundamental law of radiation. Because the sensor is designed to respond only to parallel rays of light, it responds primarily to the lamp and is not very sensitive to ambient light in the room (this is also important if we are to track the lamp). The law says that the power density (p)* from a non-coherent radiation source will be proportional to the inverse square of the distance (r) from the source, or p = k/r2 . The sensor test program displays a value of 250-255 with no lamp (lets call that the dark_ref) and the reading is reduced in proportion to the light power or intensity hitting it from the lamp, so we should expect the following relation:
Display = dark_ref – k/r2
Point the sensor at the lamp so as to minimize the reading, then move the lamp twice as far away and readjust the pointing again to minimize the reading. Does the display reading follow the 1/r2 law? Take a few points at various distances and plot the results.

2. Using the test jig and program sensa&b_cal1.c with the lamp about 35-40 cm away point each sensor at the lamp and automatically gather angular response data and plot it from each sensor. The plots should look similar to the following plots:

* power density = power per unit receiving area

3. Mount both sensors together, one on top of the other, on the test jig with a spacer near the open ends so that the top sensor is directed about 5 degrees higher than the bottom one. Adjust the angle between them, using the program display as a guide, such that the top sensor response begins to decrease (to numerically increase) at same angle that the bottom sensor response approaches its peak (numerically approaches it minimum). This alignment should allow a program which subtracts the top from the bottom sensor readings to generate a smooth function of angle which measures zero at the cross-over angle. The two sensors aligned in the above manner and subtracted create our real time angle discriminating function.

4. To verify the control capability of our angle discriminator, load aim7.c program into the Handy Board. This program will drive the test jig servo to dynamically acquire and track the light source as it is moved up and down.

/*aim7            Kevan Anderson 8/99*/

/* This program runs the servo to track the light.  Use the servo

 tracking to test your sensor characteristic.*/

void  main(){

    int pos;

    servo_on();

    pos=begin();

    track(pos);

    while(1){

        track(lost(pos) );

    }

}   

/* allows for bottom sensor to be aimed and returns that

  position*/

int begin(){

    int pos;

    while(!start_button()){

        pos= knob() ;

        printf ("angle=%d  %d\n", pos,analog(0));

        servo_deg((float)pos);

        sleep(0.5);

    }

    return(pos);

}

/* given a sensor correction and a starting position, will track a

  light sourse up and down*/

void track(int pos){

    int a; int b;

    printf("tracking\n");

    sleep(1.);

    while (!((a>250)&&(b>250))){ /* assumes sensors' dark ref > 250 */

        a= analog(0);

        b= analog(1);

        if ((a-b+1)<0){

            pos=move_down(pos);

        }

        if ((a-b-1)>0){

           pos=move_up(pos);

        }

    }

}

/* given a position where a signal is lost, will return a postion

  where a signal is found*/

 int lost(int pos){

     int i=0;

     printf("lost\n");

     while (1){

         if ((pos+i)>120){

             pos-=40;

         }

         servo_deg((float)(pos+i));

         sleep(.1);

         if ((analog(0)<250)&&(analog(1)<250)){

             return(pos+i);

         }

         if ((pos-i)<10){

             pos+=40;

         }

         servo_deg((float)(pos-i));

         sleep(.1);

         if ((analog(0)<250)&&(analog(1)<250)){

             return(pos-i);

         }

         i+=3;

     }

}

/* moves up one position, waits, then returns new position*/   

int move_up(int a){

    a++;

    servo_deg((float)(a));

    sleep(1.);

    return(a);

}

/* moves down one position, waits, then returns new position*/

int move_down(int a){

    a--;

    servo_deg((float)(a));

    sleep(1.);

    return(a);

}