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co NBS TECHNICAL NOTE 594-12

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of the Office of Measurement Services, the Office of Radiation Measurement and the following Center and divisions:

Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center

for Radiation Research: Nuclear Sciences; Applied Radiation — Laboratory Astrophysics ° — Cryogenics - — Electromagnetics " — Time and Frequency 2

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advisory and research services to other Government agencies; and develops, produces, and

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THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum

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- Located at Boulder, Colorado 80302.
Optical Radiation Measurements.

The Translucent Blurring EffectMethod of Evaluation and Estimation

Jack J. Hsia

Optical Physics Division

Institute " )v Basic Standards

National Bureau of Standards

Washington, D.C. 20234

^°F

Co,

*EA\} Of

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward O. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued October 1 976
National Bureau of Standards Technical Note 594-12

Nat. Bur. Stand. (U.S.), Tech. Note 594-12, 31 pages (Oct. 1976) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. CI 3.46:594- 12). Stock No. 003-003- Price 75 cents (Add 25 percent additional for other than U.S. mailing).
PREFACE

This is the twelfth issue of a series of Technical Notes entitled

OPTICAL RADIATION MEASUREMENTS. The series will consist primarily of

reports of progress in, or details of, research conducted in radiometry,

photometry and spectrophotometry in the Optical Radiation Section and

the Radiometric Physics Section of the Optical Physics Division.

The level of presentation in OPTICAL RADIATION MEASUREMENTS will

be directed at a general technical audience. The equivalent of an undergraduate degree in engineering or physics, plus familiarity with the

basic concepts of radiometry and photometry [e.g., G. Bauer, Measurement

of Optical Radiations (Focal Press, London, New York, 1965)], should be

sufficient for understanding the vast majority of material in this

series. Occasionally a more specialized background will be required.

Even in such instances, however, a careful reading of the assumptions,

approximations, and final conclusions should permit the non-specialist

to understand the gist of the argument if not the details.

At times , certain commercial materials and equipment will be

identified in this series in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it

imply that the material or equipment identified is necessarily the best

available for the purpose.

Any suggestions readers may have to improve the utility of this

series are welcome.

Henry J. Kostkowski, Chief Jack L. Tech, Chief

Optical Radiation Section Radiometric Physics Section

National Bureau of Standards National Bureau of Standards
TABLE OF CONTENTS

Page

1. INTRODUCTION 1

2. THE TRANSLUCENT BLURRING EFFECT 1

2.1 General Mathematical Equation . 3

2.2 Special Cases 6

2.2.1 Uniform incident flux 6

2.2.2 Concentric circular beam and port . 6

2.2.3 Misalignment 6

3. EXPERIMENTAL EVALUATIONS 8

3.1 Small Light Beam* Large Viewed Area 8

3.1.1 Instrument 8

3.1.2 Measurement and results 10

3.2 Large Light Beam* Small Viewed Area ... .10

3.2.1 Instrument 10

3.2.2 Measurement and results 10

4. PREDICTION AND VERIFICATION 14

4.1 Error Estimations 14

4.2 A Case Study - Simulation of an Actual Instrument 22

5. CONCLUSIONS AND RECOMMENDATIONS 22

6. REFERENCES 25

LIST OF FIGURES

1. Path of a photon in a diffuse reflector 2

2. A general sketch for describing the blurring phenomenon 4

3. A sketch for circular beam and mask 7

3a. Concentric 7

3b. Misaligned 7

4. The setup with small light beam and large viewed area. L = He-Ne laser;

AS = aperture stop; SF = spatial filter; MC = mirror chopper; BS = baffle

and stop; M = mask; S = sample; A,B = Detectors A and B; Amp. A,B = Amplifier

A and B; A/B = ratiometer; DVM = digital voltmeter; TTY = teletypewriter 9

5. Results of the blurring experiment on Vitrolite glass sample with the radius

of the laser beam - 0.75 mm 11

6. The setup for measuring the blurring effect with large light beam and small

viewed area 12

6a. Source 12

6b. Detector 12

W = tungsten filament source; LI, L2, and L3 = lenses; AT = aperture turrets;

IF = interference filter; S = sample; P = photometer; FT = filter turret;

PM = photomultiplier.
Page

The fraction received of Vitrolite glass sample as a function of beam radius

with different wavelengths 13

The reflected fluxes from Vitrolite glass and paint samples as a function of

distance from the light spot. (Measurements made with blue and red filters.) . . 15

Percent loss due to the blurring effect - 1 16

Percent loss due to the blurring effect -2 17

Percent loss due to the blurring effect - 3 18

Percent loss due to the blurring effect - 4 19

Percent loss as a function of the radius of the ring shape beam (ring width

= 1 mm) with masks of various radius 20

Percent loss as a function of the misalignment (with the radii of the beam and

mask being 12 mm and 18 mm, respectively) 21

Spatial sensitivity of the detector 23

Normalized flux distribution 24

THE TRANSLUCENT BLURRING EFFECT - METHOD OF EVALUATION AND ESTIMATION

Jack J. Hsia

The translucent phenomenon which causes flux loss in spectrophotometry measurements is described. Methods for mathematically evaluating

the flux loss are examined, and experimental methods using laser and con- ventional light sources are described. A widely used Vitrolite glass

standard is employed to demonstrate the error estimation and correction.

Key Words: Blurring effect; edge loss, error analysis; flux loss;

plastics; reflectance; scattering; spectrophotometry; translucency;

transmittance; Vitrolite glass.

1. INTRODUCTION

Improving the accuracy and usefulness of spectrophotometric measurements made throughout the scientific and industrial community is a fundamental purpose of the spectrophotometry

group of the Radiometric Physics Section of NBS. Increasing numbers of spectrophotometric

measurements are being made on plastic materials, and these measurements are usually based

on white glasses as measurement standards. In view of this, the possibility of measurement

error caused by flux loss resulting from the translucency [1,2,3] of the specimens deserves

close study. Such a measurement error can occur because of improper design of the instrument being used, or by not fully recognizing the limitations of the instrument. Even when

the source of error is recognized, its magnitude is sometimes underestimated.

The purposes of this Technical Note are to call attention to this often ignored error,

to derive the mathematical equations and perform measurements in order to evaluate the

magnitude of this error, to describe procedures for estimating the error, and to' recommend

methods for reducing the error.

A general equation for flux loss and equations for special cases are derived in Part 2. Several experimental setups and methods are presented in Part 3 to demonstrate how to measure

the flux loss and to show what is to be expected for its magnitude. Part 4 contains a case study describing the simulation of an actual instrument and shows how to predict flux loss

by using the general equation and experimental results from Parts 2 and 3, respectively. The

conclusions and recommendations are given in Part 5.

2. THE TRANSLUCENT BLURRING EFFECT

The reflection from a sample such as plastic or white glass can be divided into two parts: the surface reflection and the body reflection. As incident radiation strikes the

surface of the sample, it moves from the air into a medium of higher index of refraction.

At the point where the radiation passes from one medium to another, a fraction is reflected

(Fresnel reflection) . More than ninety percent of the incident flux passes through the

surface and into the sample. A small fraction of this radiation is absorbed in the material

and a large fraction of this radiation escapes after being randomly scattered within the

material. The main part of the radiation which is reflected from the sample travels this

route. One can gain an intuitive feeling for this process by thinking of the radiation in terms of photons. As is indicated in figure 1, a photon that enters at point P, moves from

one scattering point to another until at last it emerges at another point, p. The probability that the photon will emerge at a particular point decreases with the distance of that

point from the point of entry, but there is a finite possibility that the photon might emerge

at a relatively large distance from P. We will call the tendency for point irradiation of a sample to produce reflected radiation from a large area of the sample the "translucent blurring effect", and we will call the portion of the radiation that emerges from the surface of

a sample beyond the edge of the sample mask the "flux loss", since it does not contribute to the response of the receiver.

figures in brackets indicate the literature references at the end of this paper.

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2.1 General Mathematical Equation

Since details are important to a thorough analysis of a measurement, a complete definition of the measurement will be provided here. The approach to describing the measurements

and the notation used is given in detail in an NBS Technical Note [4],

The measurement to be defined will be restricted to flat samples and the directions and

locations involved in the measurement will be described in terms of a plane which coincides

with what, on a macroscopic scale, would be regarded as the surface of the sample. In this

way the complications of describing the microscopic variations in the shape of the "real"

surface are avoided. Only steady-state measurements on nonf luorescing samples will be con- sidered here, so that the definitions will not be functions of time. For simplicity, the

wavelength and polarization will not be explicitly indicated in the notation.

Under the foregoing conditions, the remaining parameters to be considered are geometrical,

involving the irradiated and viewed areas and the directions and solid angles of irradiation

and viewing. Refer to figure 2. The fraction received is defined as the ratio of the

reflected flux that is detected by the receiver from the finite area of the sample inside

the mask to the reflected flux that would be detected by the receiver from an infinitely

large area of the same sample. The percent flux loss is one minus the fraction received,

expressed as a percentage. A general expression for the fraction received can be written in

terms of the geometrical parameters in the following form:

/ / LSF

_ M

/ / LS I

LS RU«dA dfl du u«da

x

-5 (1)

LS RU«dA dfi dco u«da

where L = L(P,U) is the radiance input (incidence radiance), Sx

= Sx (P,U;p,u) is the scattering function of the sample, R = R(p,u) is the response (responsivity of the detection

system), P is a position vector denoting the point at which the radiation enters the surface,

U is a unit vector indicating the direction of entry for the radiation, dA is an element of

surface area at point P and dfi is an element of solid angle in the direction of U. The lower case variables p, u, da and dw have a similar meaning with respect to the radiation emerging

from the surface. (The sumbol f

3 is a shortened notation indicating integration with respect

to dA, dfi and dco, with each integral being taken over the full range of the corresponding

parameter.) For highly collimated radiation striking a finite area of the sample, the

radiance input can be written as

L = E(P) 6(U - U)/cosr (2)

> -*-*

where Uo is the direction of incidence, 6(Uo - U) is the Dirac delta function, ^o is the

angle between the normal to the surface and^the direction of incidence, and E(P) is the

spectral irradiance at the point P where E(P) is non-zero only over a finite area, i.e. the area being irradiated, and

/q(U) 6(U - U) dfl - q(U ) (3)

where q(U) is an arbitrary function of direction. In the case of a uniform and isotropic

translucent sample, the amount of radiation emerging from a given point from the sample

depends only on the absolute value of the displacement from the point of entry of the incoming

radiation which causes it. In this case the scattering function can be expressed as

Sx

= Sx

(r °'|p " P|. u) (4)

Further, for the case of viewing the sample by the receiver from one direction, the scattering function can be written as

3
MASK

Fig. 2. A general sketch for describing the blurring phenomenon.

4
Sx

= Sx

(r ° ; ' P "

P l» Yo) (4)

where Yo is the angle between the normal to the surface and the direction of incidence. In the ideal receiver, R is independent of position on the sample and is independent of direction

of emergence, i.e. each photon of reflected radiation produces the same contribution to the

instrument output, regardless of where it emerges or of the direction in which it emerges

within the area and solid angle from which rays are within the beam accepted by the instrument . Thus

R is constant. (5)

Inserting equations (2) and (4) in the general expression (1) for the fraction received, one

obtains:

/E(P) / Jk Jaj

i -> -> i S (r ; |p - P| , Yo) da dA

> x

S (r ; |p - P| , Yo) da dA

F = -^^

(6)

i-> -*< where fa=00 S x

(To ; J p - P|> Yo) da = C is independent of A and can be taken out of the integral

of A in the denominator. Expressing da in cylindrical coordinates, eq. (6) can be written as

F =

E (f)f H s x(r o:5 |P - P| » Yo) rdr

/e(P) dA

Jk

2tt f(r(0)) dGdA

dGdA

(7)

F--i ^

(8)

where

E(P) dA

S Y(r ;|p - P|, Yo) 2TCdr

f (r) = ^

(9)

S (r ;|p - P|, Yo) da

£

fJa=c

where f (r) is the fraction received from a circular area with radius r. f (r) , as a function

of r, can be determined experimentally and some results are presented in Part 3. Once f(r)

is known, eq. (8) gives the fraction received from any shape of area as long as r can be

expressed as a function of 0. For most of the shapes of area, it is generally difficult to perform the integration. For these cases eq. (8) can be written in terms of summations to perform computations on the computer.

(10)

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> 21T/A9 ?

f(r H M

r — ^E(?) AA
2.2 Special Cases

The general equations expressed by eqs. (8) and (10) can be simplified in the special

cases: (a) the incident flux at the sample port is uniform, (b) the sample port and light

beam are circular, and (c) the light beam is misaligned.

2.2.1 Uniform incident flux

For uniform incident flux, the irradiance is independent of the position on the sample,

i.e., E(P) = constant. Equation (8) can then be simplified

-i k Mo f(r(9)) d9 dA (ID

In order to discuss the next two special cases, the concept of the incident ring-shape

beam should be mentioned here. Refer to figure 3a. Assume the incident beam is in the shape

of a ring with width Ax and radius x and the ring is concentric with the sample port (or

mask) which has a radius m. The fraction received in this area can be expressed as:

F = x 2ttxAx

2tt

2tt f(r(0)) d0

x 2* h

2-ftxAx

f(r(0)) d9

(12)

(13)

or

Fx

= ^7A6 S f < r < » (14)

where

r = (m2 - x + x

2 cos

z 0) 2 - xcos0 (15)

2.2.2 Concentric circular incident beam and sample port (or mask)

Refer to figure 3a. For an incident beam with radius I and sample port with radius m,

eq. (11) can be written as:

tt£

2 Jo F 2iTxdx x

(16)

F = -i- Y] F 2ttxAx

tt£> 2 T x

(17)

2.2.3 Misalignment

Refer to figure 3b. When the center of the beam is misaligned and its distance from the

center of the sample port is e, the fraction received can be expressed as

F g2fTxdx

g2frxdx

(18)
MASK

0Xo= I 0M = m

OB = x BM= r

MASK

Fig. 3. A sketch for circular beam and mask

3a. Concentric

3b. Misaligned

7
or i+e

E Fx

gx

F = ik < 19 > E gx

where

Je2 + x

2 - l2 \

\

2ex )

(20)

is the fraction of the ring (with radius x and its center at the center of the mask) inside

the boundary of the misaligned incident beam.

3. EXPERIMENTAL EVALUATIONS

There are two methods to study the translucent blurring phenomenon quantitatively. The

first method is to use a radiation beam of finite size in an experiment to measure the flux

from areas with different radius, reduce the data mathematically to the case for the beam of

infinitesimal size, and then calculate cases of beams with other sizes by numerical integration. The second method is to use a beam with a very small diameter, such as a laser beam,

and calculate cases of beams with other sizes by numerical integration which requires that

a beam be divided into many small parts (or alternatively to use a large radiation beam

viewed at a very small area) . The first method calls for solving an integral equation first

for its kernel and then re-integrating [5]. The second method is much simpler since an approximation to the kernel is obtained directly. It is valid as long as, during the

numerical integration, the divided beam is not smaller than the beam size of the laser. The

second method is used to determine the values of f(r) as defined in eq. (9). Using the

second method measurements are made (a) with small radiation beam and large viewed area, and

(b) with large radiation beam and small viewed area.

Since Vitrolite white glass has a stable reflectance and a very uniform surface, it has

been used as a reflectance standard for commercial instruments and is also issued by NBS as a reflectance standard. For this reason an 11-mm-thick Vitrolite white glass sample is used

to demonstrate the experimental methods for evaluating flux loss.

3.1 Small Radiation Beam and Large Viewed Area

A laser reflectometer was used [6] . Reflected fluxes with masks of different sizes in

front of a Vitrolite glass sample were measured.

3.1.1 Instrument

The schematic diagram of the laser reflectometer is presented in figure 4. A He-Ne

laser source is operated at 632.8 nm. An aperture stop with about 2 mm diameter is placed

directly in front of the laser to block the scattered radiation surrounding the main beam.

Further filtering is accomplished by letting the beam go through a spatial filter consisting

of two quartz lenses and one 20 um diameter pinhole. The pinhole can be adjusted in a plane

normal to the beam. The first lens focuses the collimated laser beam onto the pinhole and

the second lens converts the diverging beam into a collimated beam of about 0.7 mm radius.

The mirror chopper serves to reduce background noises by using synchronous amplifiers,

as well as to modulate the final output from the detector by directing the reflected beam

from the chopper into an averaging sphere and monitor detector. The main beam passes through

a baffle to reduce stray light. The sample can be clamped on a sample holder with an opening

of 19 mm radius. A mask can be placed in front of the sample surface. Six masks are available with opening radii of 1.6, 2.4, 3.2, 4.8, 6.4, and 7.9 mm.

Lead sulfide cells with sensitive area of 10 x 10 mm were used. The field of view of

the sample detector just covers the opening of the sample holder. The signals from the
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detector A and the monitor detector B are amplified separately. The outputs of the two amplifiers are then fed into a ratiometer whose output is proportional to the ratio of the

two inputs. The ratio signal is then fed into a digital voltmeter and recorded by means of

a teletypewriter. The double-detector system ensures that the output from the digital voltmeter is independent of the drift of the laser-source output level.

3.1.2 Measurement and results

The flux reflected by a Vitrolite [7] glass sample, 76 x 76 mm and 11 mm thick, was measured with and without mask, with normal incidence and 45° viewing. All signals were

corrected for the dark signal which is the signal when the laser source is blocked. The

measuring sequence was designed to reduce the drift of the system [8],

The sample holder opening of 19-mm radius can be considered as a mask opening of

infinite radius, since the difference in reflected fluxes for larger masks is undetectable.

The fraction received was calculated by taking the ratio of the signal when measured with the

mask to the signal without the mask. The fraction received is plotted in figure 5 as a function of the radius of the mask opening and the value of 1 when the radius is 19 mm. The

solid curve was determined by fitting the data by the method of least squares to an exponential function. The choice of the exponential function is empirical. For this Vitrolite

glass sample (11 mm thick) measured with 0.7 mm radius laser beam, the fraction received

function, f(r), is as follows:

f(r) = 1 - exp(br + cr

2 + dr 3

) (21)

where r is in mm, b = -0.939, c = 0.0774, and d = -0.00299.

3.2 Large Radiation Beam* Smal I Viewed Area

3.2.1 Instrument

The fraction received by using a large radiation beam and small viewed area was measured

on a separate setup. The sketch is shown in figure 6. A tungsten light source and two lenses are used to produce a large light spot on the sample surface. The central area of 0.1 mm

diameter of the light spot is viewed by a photometer. Different sizes of light spots on the

sample surface are produced with an aperture turret containing six apertures with opening

radii of 1.5, 2.5, 3.5, 5.0, 8.0 and 12.0 mm. For the setup in figure 6a, lens L2 produced

a one to one magnification. The radius of the light spot thus could be varied from 1.5 to 12.0 mm.

Wavelength changes are made either with different interference filters in the source system or with broadband filters in the photometer. Five interference filters, with 20 nm

bandpass and with peak wavelengths at 450, 500, 550, 600, and 650 nm, are used. Three

broadband filters are used in the photometer: a blue filter with peak transmittance at 450 nm and bandpass of 60 nm, a photopic filter with peak at 550 nm and bandpass of 100 nm, and a red filter with peak at 600 nm and bandpass of 70 nm.

3.2.2 Measurement and results

At each wavelength the reflected fluxes from the Vitrolite glass sample (11 mm thick) and

white paint sample were measured at each aperture setting. The fraction received is calculated by taking the ratio of the signal when measured on the Vitrolite sample by that

measured on the white paint sample. All such ratios are normalized to the ratio at 12 mm

aperture radius. The white paint sample is chosen because its reflectance is independent

of wavelength in the visible range and it has very slight translucency compared with the

Vitrolite sample. Taking the ratio of the signals from the Vitrolite sample to that of the

white paint sample eliminates flux differences caused by changing the filter or size of the

aperture. The results are plotted in figure 7. The fraction received shows a definite

wavelength dependency. At longer wavelengths the fraction received is smaller . In other

words, the translucent blurring effect is larger at longer wavelengths. Measurements made

text continued on 'page 14 10
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BEAM RADIUS (mm)

12

Fig. 7. The fraction received of Vitrolite glass sample as a function of beam

radius.

13
with broadband filters agree with those made with interference filters.

The translucency was further measured with a light spot of 0.5 mm radius on the sample.

The small light spot is produced by replacing lens L2 in figure 6a with a lens of 90 mm

focal length and placing it 360 mm following the aperture turret. The sample was placed

120 mm beyond the lens. This setup gives a three-to-one reduction. With an aperture of

1.5 mm radius, this arrangement produced a light spot of 0.5 mm radius. The photometer is

mounted on an x-y scanner. The light spot on the sample is scanned from the center to a location 15 mm away from the center along one radius. The photometer views an area of 0.1 mm

diameter. Measurements are made on the Vitrolite glass sample (11 mm thick) and white paint

sample using blue and then red broadband filters. The results are plotted in figure 8. For

the white paint sample, measurements made with blue and red filters give the same results.

With Vitrolite glass samples, the curves show clearly that at distances away from the light

spot, the Vitrolite sample scatters more radiation flux in the red region than in the blue

region.

4. PREDICTION AND VERIFICATION

4.1 Error Estimations

The fraction received is predicted analytically utilizing eq. (17) and the function

f(r) in eq. (21) for a radiation beam of 3.2-mm radius incident on a Vitrolite sample

(11 mm thick) and masks of radii 4.8, 6.4, and 7.9 mm. The fraction received for the above

condition is also determined experimentally. The laser beam with a 3.2-mm radius is

obtained by adjusting the second lens in the spatial filter. The following table shows the

close agreement between experimental and analytical results.

Fraction Received

Mask Rad ius Experimental Analytical

(mm)

4.8 0.927 0.925

6.4 0.965 0.965

7.9 0.981 0.980

The percent loss is one minus the fraction received and expressed in percentage. Using

the equations derived in Part 2 and experimental results obtained in Part 3, we proceed to estimate what would be the fraction received or percent loss with different combinations of

beam sizes and sample-port or mask sizes.

With uniform incident-flux distribution and concentric-circular incident beam and

sample port (or mask), eqs. (21), (14), and (17) are used to generate curves of fraction

received and percent loss. Some data presented in four different ways to bring out different

relationships are shown in figures 9 and 10 in linear scales and in figures 11 and 12 in

semilog scales. For example, with beam radius of 6 mm and mask radius of 12 mm there is a loss of 0.85% and with beam radius of 12 mm and mask radius of 18 mm there is a loss of 0.39%.

Figure 11 indicates the trend with a fixed difference between the mask and beam radii, the

smaller the incident beam radius the larger the loss.

In figures 13, the percent flux loss, i.e. 1 - Fx expressed in percentage, of the Vitrolite glass (11 mm thick) is shown as a function of the radius of incident ring-shape beam

with different mask radius. Light beams are assumed to be of ring shape with various ring

radii and all with one-millimeter width. The radii of the mask openings range from 10 to

30 mm. This figure shows that the closer the light beam to the edge of the opening, the

larger the contribution to the flux loss.

In order to show how misalignment can cause an increase in flux loss, an example is

given below. For an incident beam of 13-mm radius and a sample port of 18-mm radius, the

flux loss is 0.39% as mentioned above. If the beam is misaligned by 6 mm, the edge of the

beam strikes the edge of the mask. Using the percent losses of ring-shape beams given in

figure 13 and eq. (19), the percent losses are calculated as a function of the misalignment

up to 6 mm. Results are given in figure 14. The flux loss increases rapidly when the

incident beam is approaching the mask. text continued on page 22

14
0.000

25 5.0 7.5 10.0 12.5 15.0 DISTANCE FROM CENTER (mm)-*

Fig. 8. The reflected fluxes from Vitrolite glass and paint samples as a function

of distance from the light spot. (Measurements made with blue and red

filters.)

15
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2 4 6 8 10

(MASK- BEAM RADIUS) mm >

Fig. 11. Percent loss due to the blurring effect - 3. 18
6 8 10 12 14 16 18 20 22 24 26 28 30 32

MASK RADIUS (mm) »>

Fig. 12. Percent loss due to the blurring effect - 4. 19
co

CO

o

a*

5 10 15 20

BEAM RING RADIUS (mm)

25 30

Fig. 13. Percent loss as a function of the radius of the ring shape beam (ring width

= 1 mm) with masks of various radius.

20
2.0

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1.0

0.0

BEAM RADIUS = 12 mm

SAMPLE PORT RADIUS = 18 mm

I I 1 2 3 4 5 6

MISALIGNMENT (mm)

Fig. 14. Percent loss as a function of the misalignment (with the radii of the beam

and mask being 12 mm and 18 mm, respectively)

.

21
A commercial 45°/0° reflectometer has been evaluated and simulated in order to predict

the percent flux loss if a Vitrolite glass is measured.

The detector response R and irradiance E(P) as a function of location on the sample

surface were determined by using a mapping technique. For the measurement of R, the light

source of the instrument was blocked and an external source was used to do the mapping.

Refer to figure 15. A thin opal glass was placed on an aperture plate which has a 6.4-mmdiameter opening. The ambient light source was irradiated on the opal glass to generate

diffuse light. The unit containing the opal glass and the aperture plate was moved on the

sample port, so that the aperture opening could be positioned at any location in the sample

plane. Nine positions are chosen to do the mapping. Their actual positions and the spatial

response of the detector in arbitrary units are shown in figure 15. The results indicate

that the spatial response is fairly uniform.

-> The irradiance distribution, E(P), on the sample plane, of the light source was mapped

by using an external detector. A silicon cell, with 1 mm

2 sensitive area, was positioned by

an x-y scanner on the sample port. The normalized irradiance distribution of the incident

light beam at the sample port is shown in figure 16 which indicates some scattered light

surrounding the main beam. The values of E(P) from the mapping and f(r) from eq. (21) are used in eq. (8) to perform the numerical integrations. The fraction received calculated is

0.978. Thus the flux loss due to the translucent effect is 2.2%.

A round robin intercomparison of a flat paint sample was conducted by NBS [4]. One of

the participating laboratories used an instrument similar to the above mentioned reflectometer and used Vitrolite glass as the standard. The results obtained by that laboratory

differed from those obtained at NBS by about 2%, indicating that translucency of the white

standard might be the major cause of the error.

5. CONCLUSIONS AND RECOMMANDATIONS

With translucent materials such as plastics and white glasses, the loss due to translucent effect can be a big contribution to the spectrophotometric measurement error.

Methods for mathematically evaluating the flux loss are examined. Equations are derived

for several special cases such as uniform irradiance, concentric incident beam and sample

port, and misalignment. An experimental setup and methods have been described to show how

to evaluate the translucent effect or percent loss quantitatively. Results are given for an 11-mm thick Vitrolite white glass. Several sets of curves of flux loss prediction are presented for a combination of different sizes of the radiation beam and sample port. An

actual reflectometer has been simulated and the error due to translucency predicted.

The information presented here can be used to calculate flux loss corrections when a Vitrolite standard is used.

From this study, several recommendations can be made in connection with making spectrophotometric measurements of translucent materials:

(a) Reduce scattered radiation surrounding the main beam;

(b) The size of the sample port should be at least two to three times

larger than that of the main beam;

(c) Use large samples;

(d) Align the radiation beam to the center of the sample port;

(e) Be aware of possible error of measurements due to flux loss; and

(f) Correct for translucency or flux loss if possible.

22
SAMPLE PORT

2 3

4 5 6

7 8 9

SAMPLE PORT

LIGHT

6.4 mm dia.

OPAL GLASS

(Imm thick)

APERTURE PLATE

(0.5 mm thick)

POSITION

* FLUX POSITION

* FLUX POSITION * FLUX

1 3.12 2 3.06 3 2.79

4 3.38 5 3.32 6 3.03

7 3.02 8 3.00 9 2.70

* ARBITRARY UNIT

Fig. 15. Spatial sensitivity of the detector.

23
0.0067

0.067

0.67

0.17

0.017

SAMPLE PORT

Fig. 16. Normalized flux distribution.

24
6. REFERENCES

1. Hunter, R. S., A Multipurpose Photoelectric Reflectometer, J. Opt. Soc. Am. 30, 536

(1940).

2. Judd, D. B. , and Wyszecki, G. , Color in Business, Science and Industry, John Wiley and

Sons, Inc., New York, N.Y. , 2nd ed. , 1963, pp. 102-103.

3. Atkins, J. T. , and Billmeyer, F. W. , Jr., Edge-Loss Errors in Reflectance and Transmittance Measurement of Translucent Materials, Materials Res. and Std. 6, 564 (November

1966).

4. Venable, W. H. Jr., and Hsia, J. J., Describing Spectrophotometric Measurements, Nat.

Bur. Stand. (U.S.), Tech. Note 594-9, (November 1974).

5. Venable, W. H. Jr., Effects Upon Radiant Intensity Measurements Due to Scattering by

Optical Elements, Appl. Opt. 9_, 609 (March 1970).

6. Hsia, J. J., and Richmond, J. C. , A High Resolution Laser Bidirectional Reflectometer

with Results on Several Optical Coatings, J. Res. Nat. Bur. Stand. (Physics and

Chemistry) 80A (2), March-April 1976.

7. Certain commercial instruments or materials are identified in this Technical Note in

order to specify adequately the procedure. In no case does such identification imply

endorsement or evaluation by the National Bureau of Standards.

8. Hsia, J. J., Optical Radiation Measurements: Th.e NBS 20-, 60-, and 85-Degree Specular

Gloss Scales, Nat. Bur. Stand. (U.S.) Tech. Note 594-10, (July 1975).

25
WBS-TTW< rev; 7-731

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

flZBS TN-594-1 P,

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

OPTICAL RADIATION MEASUREMENTS:

THE TRANSLUCENT BLURRING EFFECT - Method of Evaluation and

Estimation

5. Publication Date October 1976

6. Performing Organization Code

7. AUTHOR(S)

Jack J. Hsia

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same

13. Type of Report & Period CoveredFinal

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less tactual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.)

The translucent phenomenon which causes flux loss in the spectrophotometric

measurement is described. Methods for mathematically evaluating the flux loss are examined, and experimental methods using laser and conventional light sources are described. A widely used Vitrolite glass standard is employed to demonstrate

the error estimation and correction.

17. KEY WORDS fsi'x ro twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Blurring effect; edge loss; error analysis; flux loss;

plastics; reflectance; scattering; spectrophotometry; translucency; transmittance;

Vitrolite glass.

18. AVAILABILITY Hxl Unlimited

I | For Official Distribution. Do Not Release to NTIS

| xl Order From Sup. of Doc, U.S. Government Prmtine Office Washington, D.C. 20402, SD Cat. No. CI 3 .46: 594-12

_J Order From National Technical Information Service (NTIS)

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