BasicsOfPhotometry_NguyenDang_e1500966

Information Technology Degree Program

Principal of Modern Physic Laboratory Exercises

Lab No 4 – Basics of Photometry

Laboratory performed on

26/01/2016

Nguyen Hai Dang

Partner: Do Tuan Minh, Nguyen Cong Danh

Team: 4

Class: I-IT-1N2

Date: 15/02/2016

_____________________________________

BASICS of PHOTOMETRY Nguyen Hai Dang 2 | P a g e

CONTENTS

ABSTRACT……………………………………………………………………….3

I. INTRODUCTION ............................................................................................ 4

II. EXPERIMENT PROCEDURE ........................................................................ 6

III. EXPERIMENTAL RESULTS ......................................................................... 9

IV. ANALYSIS .................................................................................................... 10

Experiment 1: The luminous Efficiency ......................................................... 10

Experiment 2: The Reflectivity ...................................................................... 13

V. DISCUSSION ................................................................................................. 14

VI. CONCLUSION .............................................................................................. 19

VII. REFERENCES .............................................................................................. 19

VIII. APPENDICES .............................................................................................. 20


Abstract

Two experiments had been carried out with an aim to grasp the four basic photometric

quantities: luminous flux, luminous intensity, illuminance and luminance. In the first

experiment, luminous intensity of an incandescent lamp as a function of direction angle

had been recorded by the lux-meter, which was then utilized to calculate the total

luminous flux, Φ��, which had been found 437.85 lm. Consequently, the luminous

efficiency of the light bulb had been found 11.58 lm/W and then compared with that of

other common types of light bulbs. In the second experiment, the coefficient of

reflectivity had been found for 10 different cardboards of the same texture but different

colors with the measurements of illuminance incident on the cardboards and their

luminance. The explanation for the coefficient of reflectivity in association with the

apparent brightness of the cardboards and the lighting conditions of the laboratory

environment had been attempted. Furthermore, this work also discusses corresponding

radiometric quantities of photometric quantities and the conversion between those

corresponding quantities. In addition, the second laboratory experiment can be

improved by implementation of strictly controlled lighting source that emulates black

body radiators.


I. INTRODUCTION

Radiometry is the science that characterizes any portion of the electromagnetic

spectrum. Using radiometric units, electromagnetic radiation can be described in terms

of physical quantities such as wavelengths, photon energies and optical power.

However, when it comes to light perceived by human beings, such quantities become

irrelevant. This is where Photometry comes into the play, as photometric quantities

characterize the light causing color sensation to the human eye. Four important

photometric quantities are luminous intensity, luminous flux, illuminance, and

luminance.

The luminous intensity describes the light intensity of an optical source as perceived

by human eyes. The unit of luminous intensity is the candela (cd), which is a SI unit.

The present definition of luminous intensity is as follows: a monochromatic light

source emitting an optical power of (1/683) watt at 555 nm into the solid angle of 1

steradian (sr) has a luminous intensity of 1 candela (cd).

The luminous flux characterizes the light power of a light source meaningful to human

vision. The luminous flux is quantified in SI units of lumen (lm). Here follows the

definition of this photometric quantity: a monochromatic light source emitting an

optical power of (1/683) watt at 555 nm has a luminous flux of 1 lumen (lm). Two

above mentioned definitions imply that 1 candelas equals 1 lumen per steradian, or

�� = ��/��.

The illuminance represents the luminous flux incident per unit area. This photometric

quantity is measured in lux (�� = ��/��). This SI unit is useful when describing

illumination conditions. For example, illumination condition of full moon is 1 lux, and

of direct sunlight is 100000 lux.


The luminance of a surface source is the ratio of the luminous intensity emitted in a

certain direction divided by the projected area in that direction. Hence the unit of

luminance is ��/��.

In addition, luminous efficiency of a light source is a photometric quantity that

describes the efficiency of conversion from electrical input power to the total luminous

flux of that source:

�� = Φ��

�

Furthermore, this laboratory exercise covered coefficient of reflectivity of a surface

when it is illuminated by a certain lighting condition. The coefficient of reflectivity of

a surface is defined with the luminance of that surface, L, and the illuminance incident,

E, at the surface by mean of the following equation:

� = ��

�

The coefficient of reflectivity is a unit-less quantity with the value inside the range 0

and 1.


II. EXPERIMENT PROCEDURE

There was two major experiments in this laboratory exercise.

The first experiment: The Luminous Efficiency

This experiment had been performed inside the dark room.

An incandescent lamp manufactured had been powered by 230 Vrms

voltage. In addition, two digital multi-meters were devised to measure

voltage across the lamp and the current running through it. The lamp

was placed on a rotatable stand, and it was placed at a fixed distance of

50 cm away from the sensor of the lux meter.

Rotate the stand of the lamp in 10° step from 0° (when lamp directly

faced the meter) to 180° (when the lamp had its full back on the

meter). In each rotating step, the value of illuminance E from the

meter was recorded.

Figure 1. Wiring of the light bulb


Figure 2. The Lux-meter and its sensor

Figure 3. The lamp had been placed on a rotatable stand. The bulb had been 50cm away from the lux-sensor.


The second experiment: The Reflectivity

This experiment had been performed outside the dark room.

The paper sample packet was placed onto a horizontal surface, which

was well illuminated by the lighting system in the laboratory.

Magnitude of illuminance incident on the paper packet was measured

by lux-meter.

The luminance sensor had been fastened to the metal bar attached to

the rigid stand so that it was directed toward the paper packet at 45°

angle.

Magnitude of the luminance of the paper of different colors had been

recorded from the luminance meter.

Figure 4. The reflectivity experiment


III. EXPERIMENTAL RESULTS

Experiment 1: The Luminous Efficiency

Electrical input current and voltage: � = 0.164� , � = 230.5�

The distance from the light source to the flux sensor: � = 0.5 �

Table 1. Luminous intensity as a function of direction angle

�/° 0 10 20 30 40 50 60 70 80 90

E/lux 124.2 124.6 125.9 128.47 132.9 138.2 143.9 149.3 154.3 157.4

�/° 100 110 120 130 140 150 160 170 180

E/lux 158.8 157.3 149.9 137.7 120.3 98.9 76.8 58.1 47.6

Experiment 2: The Reflectivity

Illuminance incident on the paper packet: � = 430 ��

The luminance value L for the each sample paper of different colors:

Table 2. Luminance of the paper of the same texture but different color

Color White Yellow Orange Gray Red

�/��

��

133.1 112.1 74.5 66.1 33.4

Color Green Army Green Navy Dark blue Black

�/��

��

33.2 23.6 20.0 12.5 10.3


IV. ANALYSIS

Experiment 1: The luminous Efficiency

In this experiment, the light source had been approximated as a point-like source.

Hence the luminous intensity of the lamp as a function of the direction angle � can

be calculated by mean of the following equation:

��(�) = �� × ��

Given the luminous intensity as the function of direction angle, �, the corresponding

��(�) for the light source was plotted by the utilization of Mathcad software:

Figure 5. I�(θ) curve for the light source

In this graph, the point-like source has it position at (0, 0) point in the coordinate.

The total luminous flux, Φ��, then can be determined by mean of the following

function:

Φ�� = 2� � ��(�) sin(�) ��

�

= 437.85 ��


Electrical input power of the light source:

� = �. � = 230.5� × 0.164� = 37.80 �

Finally, we arrive at luminous efficiency of this lamb:

� =Φ��

�= 11.58

��

�

To make this obtained value make sense, we compare this the luminous efficiency of

this lamb with one type of fluorescent lambs, namely Bright white 2X, which has the

following properties:

Table 3. Luminous efficiency of one type of fluorescent lambs

P/W Φ��/lm Luminous efficiency / (lm/W)

15 580 38.7

20 820 41

30 1500 50

40 2100 52.5

80 3900 49

Conclusion: our tungsten filament lamp has luminous efficiency more than three

time lower than that of Bright white 2X fluorescent lambs.


This should be of no surprise given the following luminous efficiency of common

light sources table:

Table 4. Luminous efficiency of different light source. (I) Incandescent sources. (II) Fluorescent sources. (III) High-intensity discharge (HID) sources

Light Source Luminous Efficiency/(lm/W)

(I) Edison’s first light bulb (C filament) 1.4

(I) Tungsten filament light bulbs 15-20

(I) Quartz halogen light bulbs 20-25

(II) Fluorescent light tubes and compact bulbs 50-80

(III) Mercury vapor light bulbs 50-60

(III) Metal halide light bulb 80-125

(III) High-pressure sodium vapor light bulbs 100-140


Experiment 2: The Reflectivity

The experimentally determined values of illuminance incident on the sample packet,

E, together with the luminance of the paper, L, has helped us arrive at the coefficient

of the reflectivity, �, whose value is between 0 and 1:

Table 5. Coefficient of reflectivity of cardboards

Color White Yellow Orange Gray Red

� 0.97 0.82 0.54 0.48 0.24

Color Green Army Green Navy Dark blue Black

� 0.24 0.17 0.15 0.09 0.08

It is obvious that the apparent brightness is indicated by the coefficient of reflectivity:

given the same illuminance incident on the surface and the same relative position of

observation, the surface looks brighter if it has bigger coefficient of reflectivity. For

instance, black surface with the lowest coefficient of reflectivity is the darkest surface,

whereas the white surface with the highest coefficient of reflectivity looked the

brightest one without doubts. In addition, yellow surface looked brighter than an orange

surface, as indicated by their coefficient of reflectivity.


V. DISCUSSION

Photometry is one branch of Radiometry dealing solely with electromagnetic radiation

perceived by human eye. That means photometric quantities have corresponding

radiometric quantities, which are summarized in the following table:

Table 6. Photometric unit and its corresponding radiometric unit

Photometric unit Dimension Radiometric unit Dimension

Luminous flux lm Radiant flux

(optical power)

W

Luminous intensity cd=lm/sr Radiant intensity W/sr

Illuminance lux=lm/m2 Irradiance

(power intensity)

W/m2

Luminance cd/m2=lm/(sr×m2) Radiance W/(sr×m2)

Problems rise as scientists want the conversion between radiometric and photometric

units. The solution has been the luminous efficiency function or eye sensitivity

function or luminosity function, �(λ). This function describes the average spectral

sensitivity of human visual perception of brightness. Because it was constructed

based on subjective judgements of the brighter source between two different-colored

lights to describe the relative sensitivity to light of different wavelengths, it should

not be deemed perfectly precise in every case. However, Luminosity function is a

very good representation of visual sensitivity of the human eye.


Figure 6. Eye sensitivity function V(�)

For wavelengths of the range 390nm to 720nm, the luminous efficiency function

�(λ) is greater than 0.001. That means the human eye’s sensitivity to light with

wavelengths outside this range is extremely low. As a result, the wavelength ranging

from 390nm to 720nm can be considered the visible wavelength range, which is a

small portion or radiometric wavelength ranges that Photometry deals with.

The total luminous flux can be obtained from the radiometric light power using the

following equation:

Φ�� = 683��

�� (λ)P(λ)dλλ

Where P(λ) is the power spectral density, which describes light power emitted per

unit wavelengths.


Total luminous flux when divided by the total optical power emitted by a light source

gives the energy portion of the total optical power meaningful to human vision, or the

luminous efficacy of optical radiation.

�� =Φ��

�= �683

��

�� (λ)P(λ)dλ

λ

� / �� (λ)�λ

λ

�

In this following part of discussion, I attempted to give explanation for the

experimental result of coefficient of reflectivity. Obviously, Artificial light sources in

our laboratory environment did not have the same spectral distribution as a perfect

back body did. However for simplicity, I assumed that the Reflectivity experiment

had been carried out with black body radiator at the temperature of T=2045K as a

light source.


Integration of the product of the �(λ) function with the black body radiation function

when multiplied by the normalizing factor 683��

� provided us with the total luminous

flux.

Each frequency range is associated with a certain color, which is described in the

following table:

Table 7. Color and associated wavelength ranges


From the luminous flux distribution function and the given color associated with a

certain range of wavelength, we can possibly visualize that yellow is the color that

contributes the most luminous flux. It is the fact that the yellow paper appear yellow

because such paper diffusely reflects electromagnetic waves associated with yellow

range while absorbing the light of other wavelengths. Hence the yellow paper

appeared brighter than red paper did for the large part because yellow light provided

richer luminous flux than red light did. Furthermore, white paper appeared the

brightest of all since it almost absorbed very little visible incident lights, whereas

black paper appeared the darkest of all since it absorbed almost all visible incident

lights. In addition, the cardboards in this experiment had been made of the same

texture but different color because it guaranteed the similar absorption and reflection

properties of the cardboard with respect to the probability distribution of the diffusion

of light, making our comparison more valid.

Up to this point of discussion, it can be seen that the explanation for the reflectivity of

papers of the same texture but different colors can be specifically provided if the

lighting condition in this experiment be controlled so that the spectral and power

distribution characteristic to such light source is not unknown. For example, the light

source can emulate the black body radiators. This is one possible way of improving

this laboratory experiments.


VI. CONCLUSION

Photometry is the science of the measurement of light with respect to its usefulness to

human vision. Through this laboratory exercise, four photometric quantities: luminous

flux, luminous intensity, illuminance and luminance, had been clearly exposed along

with luminous efficiency and coefficient of reflectivity of surface.

VII. REFERENCES

[1]Mark S.Rea (editor-in-chief). Lighting Handbook. 1993.

[2]Raymond A.Serway and John W.Jewett, Jr. Physics for Scientists and Engineers

with Modern Physics.

[3]Richard Wolfson and Jay M.Pasachoff. Physics with modern physics for scientists

and engineers.


VIII. APPENDICES

Documents

BasicsOfPhotometry_NguyenDang_e1500966