National Aeronautics and

Space Administration

IS20

George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama

35812
The NASA STI Program...in Profile

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientific and Technical Information (STI) 

Program Office plays a key part in helping NASA 

maintain this important role.

The NASA STI Program Office is operated by 

Langley Research Center, the lead center for 

NASA’s scientific and technical information. The 

NASA STI Program Office provides access to 

the NASA STI Database, the largest collection of 

aeronautical and space science STI in the world. 

The Program Office is also NASA’s institutional 

mechanism for disseminating the results of its 

research and development activities. These results 

are published by NASA in the NASA STI Report 

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major significant 

phase of research that present the results of 

NASA programs and include extensive data 

or theoretical analysis. Includes compilations 

of significant scientific and technical data 

and information deemed to be of continuing 

reference value. NASA’s counterpart of peerreviewed formal professional papers but has less 

stringent limitations on manuscript length and 

extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific 

and technical findings that are preliminary or of 

specialized interest, e.g., quick release reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis.

• CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientific and technical conferences, 

symposia, seminars, or other meetings sponsored 

or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientific, technical, 

or historical information from NASA programs, 

projects, and mission, often concerned with 

subjects having substantial public interest.

• TECHNICAL TRANSLATION. 

English-language translations of foreign 

scientific and technical material pertinent to 

NASA’s mission.

Specialized services that complement the STI 

Program Office’s diverse offerings include creating 

custom thesauri, building customized databases, 

organizing and publishing research results...even 

providing videos.

For more information about the NASA STI Program 

Office, see the following:

• Access the NASA STI program home page at 

<http://www.sti.nasa.gov>

• E-mail your question via the Internet to 

<help@sti.nasa.gov>

• Fax your question to the NASA STI Help Desk 

at 443 –757–5803

• Phone the NASA STI Help Desk at 

443 –757–5802

• Write to:

NASA STI Help Desk

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076–1320
i

NASA/TM—2011–216464

Figures of Merit Software: Description, 

User’s Guide, Installation Notes, Versions 

Description, and License Agreement

H.D. Hoelzer and K.A. Fourroux

Teledyne Brown Engineering, Inc., Huntsville, Alabama

D.L. Rickman

Marshall Space Flight Center, Marshall Space Flight Center, Alabama 

C.M. Schrader

BAE Systems, Huntsville, Alabama

March 2011

National Aeronautics and

Space Administration

Marshall Space Flight Center • MSFC, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076 –1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov>

TRADEMARKS

Trade names and trademarks are used in this report for identification only. This usage does not constitute an official 

endorsement, either expressed or implied, by the national Aeronautics and Space Administration.
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

2. DEFINITIONS .................................................................................................................. 3

2.1 Reference and Simulant Materials ................................................................................ 3

2.2 Definition of Discrete Category Functions ................................................................... 3

2.3 Relative Frequency Distribution Functions .................................................................. 5

3. FIGURE OF MERIT DESCRIPTIONS ........................................................................... 9

3.1 Modal Composition ..................................................................................................... 9

3.2 Particle Size Distribution .............................................................................................. 9

3.3 Particle Shape Distribution ........................................................................................... 9

3.4 Density ......................................................................................................................... 10

4. SOFTWARE DESCRIPTION ........................................................................................... 11

4.1 Software Inputs ............................................................................................................ 11

5. DATA ENTRY FOR THE FIGURE OF MERIT SOFTWARE ....................................... 12

5.1 Introduction ................................................................................................................. 12

5.2 Structure of the Data Files ........................................................................................... 12

5.3 Worksheet Definitions .................................................................................................. 13

5.4 Creating a Reference or Simulant Data File .................................................................. 28

6. USING THE FREQUENCY OF MERIT SOFTWARE ................................................... 31

6.1 Selecting Reference and Simulant Data Files for Figure of Merit Calculations ............ 31

6.2 Computing Figures of Merit ........................................................................................ 32

6.3 Figure of Merit Messages and Saving Results .............................................................. 46

6.4 Figure of Merit Menu Descriptions .............................................................................. 48

6.5 Plot Windows Help ...................................................................................................... 50

6.6 Limitations of Using Excel With the Figure of Merit Software .................................... 55

6.7 Copyrights .................................................................................................................... 56
iv

TABLE OF CONTENTS (Continued)

 7. INSTALLATION NOTES ............................................................................................... 57

7.1 Minimum System Requirements ............................................................................... 57

7.2 Required Components for Execution of Figure of Merit Software ........................... 57

7.3 Installation Instructions ............................................................................................ 58

7.4 Installation of MATLAB Compiler Runtime ........................................................... 58

7.5 Specific Steps ............................................................................................................ 59

7.6 Installation of Figure of Merit Software ................................................................... 64

7.7 Specific Steps ............................................................................................................ 64

7.8 Messages/Errors ........................................................................................................ 67

7.9 Uninstallation of the Figure of Merit Software ........................................................ 69

7.10 Uninstallation of the MathWorks MATLAB Compiler Routine ............................... 69

 8. TROUBLESHOOTING ................................................................................................... 70

8.1 Installation Troubleshooting ....................................................................................... 70

8.2 Execution Troubleshooting ......................................................................................... 70

 9. VERSION DESCRIPTION DOCUMENT ...................................................................... 72

9.1 Figure of Merit Software Version ............................................................................... 72

9.2 Figure of Merit Software Package Components ......................................................... 72

9.3 Ancillary Software (Development Environment) ........................................................ 75

10. SUPPORT ......................................................................................................................... 77

10.1 About Figures of Merit Software .............................................................................. 77

11. CONTACT INFORMATION .......................................................................................... 78

12. LICENCES FOR THE FIGURES OF MERIT SOFTWARE ......................................... 79

12.1 License Agreement .................................................................................................... 79

12.2 Freeware ................................................................................................................... 79

12.3 Components .............................................................................................................. 79

12.4 Disclaimer of Warranty ............................................................................................ 79

12.5 Use and Restrictions ................................................................................................. 80

REFERENCES ....................................................................................................................... 83
v

LIST OF FIGURES

 1. Example discrete category function showing composition 

for a hypothetical material ....................................................................................... 4

 2. Example cumulative (a) and relative (b) frequency distributions for particle size

of a hypothetical material ........................................................................................ 6

 3. Example data entry field .......................................................................................... 12

 4. Example computation field ...................................................................................... 12

 5. Example help ........................................................................................................... 13

 6. Example linked data field ........................................................................................ 13

 7. Description worksheet ............................................................................................. 14

 8. Modal Composition—Minerals worksheet .............................................................. 15

 9. Modal Composition—Minerals example ................................................................. 17

10. Modal Composition—General worksheet ............................................................... 18

11. Modal Composition—General example .................................................................. 20

12. Size Distribution worksheet ..................................................................................... 21

13. Size Distribution example ........................................................................................ 22

14. Shape—Aspect Ratio worksheet .............................................................................. 23

15. Shape—Aspect Ratio example ................................................................................. 25

16. Shape—Angularity worksheet ................................................................................. 25

17. Shape—Angularity example .................................................................................... 27

18. Density worksheet ................................................................................................... 28

19. Density example ...................................................................................................... 29
vi

LIST OF FIGURES (Continued)

20. Reference and Simulant data file selection fields ...................................................... 31

21. Selection of a reference material data file ................................................................. 32

22. Filled in fields for reference and simulant material data files .................................... 32

23. Color change indicating a selection ......................................................................... 33

24. Modal Composition—Minerals FoM dialog box .................................................... 34

25. Size Range Mis-match warning dialog box .............................................................. 34

26. Modal Composition—Minerals reference and simulant bar graphs ......................... 35

27. Modal Composition—Minerals joint and difference bar graphs .............................. 36

28. Modal Composition—Minerals data tree view ........................................................ 37

29. Window menu ......................................................................................................... 38

30. Modal Composition—Minerals tree control menu .................................................. 38

31. Modal Composition—General FoM dialog box ...................................................... 39

32. Size Distribution FoM dialog box ........................................................................... 39

33. Size Distribution histogram plots ............................................................................ 40

34. Shape—Aspect Ratio FoM dialog box ..................................................................... 41

35. Shape—Aspect Ratio FoM graphics output ............................................................ 42

36. Shape—Angularity FoM dialog box ........................................................................ 43

37. Shape—Angularity FoM graphics output ................................................................ 43

38. Density FoM dialog box .......................................................................................... 44

39. Density FoM graphics output, page 1 ...................................................................... 45

40. Density FoM graphics output, page 2 ...................................................................... 45
vii

LIST OF FIGURES (Continued)

41. FoM Messages window ........................................................................................... 46

42. Window menu ......................................................................................................... 46

43. Options menu .......................................................................................................... 47

44. FoM File menu ........................................................................................................ 48

45. FoM Window menu ................................................................................................. 49

46. FoM Help menu ...................................................................................................... 49

47. File menu ................................................................................................................. 50

48. FoM plot windows Graph menu .............................................................................. 51

49. FoM plot windows Labels dialog box ...................................................................... 52

50. Axis Scaling dialog box ........................................................................................... 53

51. Gallery menu ........................................................................................................... 54

52. Plot toolbar ............................................................................................................. 54

53. Excel is already running error message .................................................................... 56

54. MATLAB responds with version information ......................................................... 58

55. MCRInstaller .......................................................................................................... 59

56. Choose Setup Language .......................................................................................... 59

57. InstallShield Wizard MATLAB(R) ......................................................................... 59

58. InstallShield Wizard (prepare to install) .................................................................. 60

59. Windows Installer .................................................................................................... 60

60. MATLAB(R) Compiler Runtime 7.9 ....................................................................... 61

61. MATLAB(R) Customer Information ...................................................................... 61
viii

LIST OF FIGURES (Continued)

62. MATLAB(R) Destination Folder ............................................................................ 62

63. MATLAB(R) Ready to Install the Program ............................................................ 62

64. Installing MATLAB(R) Computer Runtime 7.9 ...................................................... 63

65. Installing MATLAB(R) Computer Runtime (.NET Framework not installed) ....... 63

66. MATLAB(R) Installation Wizard Completed ......................................................... 64

67. FoM setup Installer ................................................................................................. 64

68. Figures of Merit ...................................................................................................... 65

69. Destination Directory .............................................................................................. 65

70. License Agreement .................................................................................................. 66

71. Start Installation ...................................................................................................... 66

72. Overall Progress ....................................................................................................... 67

73. Installation Complete .............................................................................................. 67

74. .NET Framework is not installed ............................................................................. 68

75. Unable to Locate Component ................................................................................. 68

76. Microsoft Excel Automation ................................................................................... 69

77. Excel Launch Error ................................................................................................. 69

78. Unable to locate FoM DLL error message ............................................................... 70

79. Path depth error message.......................................................................................... 71
ix

LIST OF TABLES

 1. Plot toolbar icon names and functions .................................................................... 55

 2. DLL package ........................................................................................................... 72

 3. Matlab FoM DLL primary components .................................................................. 72

 4. Matlab FoM DLL support components .................................................................. 73

 5. LabWindows/CVI primary components .................................................................. 73

 6. LabWindows/CVI support components .................................................................. 73

 7. Files that comprise Version 2.0 of the FoM application code .................................. 74

 8. FoM Matlab DLL (FoM_Matlab.dll) Version 2.6 .................................................... 74

 9. Excel workbook version number .............................................................................. 74

10. Document version numbers ..................................................................................... 75

11. Compile script ......................................................................................................... 75

12. MathWorks software ............................................................................................... 75

13. Workspace and project files ..................................................................................... 76

14. National Instruments software ................................................................................ 76
x

LIST OF ACRONYMS AND SYMBOLS

3-D three-dimensional

Ca calcium

CaAl2Si2O8 anorthite

CFD cumulative frequency distribution

CVI C for Virtual Instrumentation

DC discrete category 

DLL dynamic link library

Fe iron

FoM figure of merit

ITAR International Traffic in Arms Regulations

MCR MATLAB Compiler Runtime

MSFC Marshall Space Flight Center

NaAlSi3O8 albite

RFD relative frequency distribution

RTE run-time environment

TBE Teledyne Brown Engineering

TM Technical Memorandum

U.S. United States
1

TECHNICAL MEMORANDUM

FIGURES OF MERIT SOFTWARE: DESCRIPTION, USER’S GUIDE, INSTALLATION 

NOTES, VERSIONS DESCRIPTION, AND LICENSE AGREEMENT

1. INTRODUCTION

The surfaces of rocky planets, moons, and some other astronomical bodies have significant 

amounts of broken geologic materials. In the absence of more specific, applicable terminology, 

such materials are generically termed regolith. Even on relatively simple bodies like the Moon, the 

nature of regolith is fairly complex. For space mission development, a regolith needs to be simulated, and many regolith simulants have been created for the Moon and Mars.

Therefore, the choice of simulant and its performance are significant considerations. An 

engineer specifying, procuring, or using a simulant needs to know how accurately the simulant 

replicates the actual regolith. Geologists do not have a relevant standard method for such comparisons. Those who have listened to lunar geology experts publically argue whether a simulant is good 

know that expert opinion, lacking quantifiable criteria, can be a very poor basis for making engineering decisions, but making such a comparison is nontrivial. Regoliths are complex and highly 

variable mixtures of many constituents; there are wide variations in most properties at almost all 

sampling scales.

Figures of Merit (FoMs) and FoM software provide a method for evaluating the quality of 

a regolith simulant by comparing the simulant to a reference material. FoMs are concepts new to 

simulant development that may be used for comparing a simulant to an actual regolith material, for 

a specification by stating the value a simulant’s FoMs must attain to be suitable for a given application, and for comparing simulants from different vendors or production runs. FoMs may even be 

used to compare different simulants to each other.

A single FoM is conceptually a defined procedure for comparison of functionally identical measures made on two different materials. As implemented in an algorithm, a single number is 

computed to quantify the similarity or difference of that single characteristic of a simulant material 

and a reference material. Therefore, it provides a clear, unambiguous, standardized measure of how 

well a simulant and reference material match or compare. As a practical aid in their use, FoMs have 

been constructed to lie between zero and 1, with zero indicating a poor or no match and 1 indicating a perfect match.

Four top-level characteristics and several lower level characteristics for comparing materials 

have been defined for which FoMs may be computed. These characteristics are as follows:
2

• Modal composition:

 – Minerals.

 – General.

• Particle size distribution.

• Particle shape distribution:

 – Aspect ratio.

 – Angularity.

• Density.

An FoM may be constructed from multiple, more detailed FoMs. For example, one can 

have an FoM for modal composition and an FoM for each mineral considered under modal composition.

For additional explanation of the underlying concepts and motivations, the reader is 

directed to references 1, 2, and 3. The concepts implemented in the FoM software are also the basis 

of an ISO standard for lunar simulants.4

The FoM software is a computer software implementation of the FoM algorithms and may 

be used to compute the FoMs. The software was created for two reasons. There was a need to prove 

that concepts embodied in the FoMs were fully consistent and realizable. As any inventor knows, it 

is one thing to have an idea; it is another to make it into a reality. It was through this prudent exercise that several problems were identified and corrected. Second, there was a need to actually make 

the necessary comparisons and there is more computational and data management burden than 

one should do without dedicated software.

It should be noted that the FoM software only computes a set of numbers (the FoMs) that 

indicate how well a simulant material matches a reference material. It does not say anything about 

how well a simulant is suited for a particular application or purpose. The user of the software must 

make that determination. Further, the FoM software does not contain any data; it is only a computational engine that computes FoMs from data supplied by a user.

The existing FoM code is not a full implementation of the essential concepts. It is missing 

some details, such as the handling of contaminants and intricacies related to solid solutions. It also 

does not deal with spectroscopy, which will need to be added in the future. But, there is no serious 

question that the implementation contained in this release is a massive revolution in evaluation and 

comparisons of lunar regolith and simulants.
3

2. DEFINITIONS

2.1 Reference and Simulant Materials

An FoM algorithm is a method for comparing two materials. These are given the labels 

Reference material and Simulant material, but this labeling is arbitrary and does not factor into the 

computation. It is done only to provide handles for the two materials being compared. Normally, 

one would consider the reference material to be an actual material that one is trying to replicate or 

simulate. However, a reference material may be completely hypothetical.

A simulant is usually considered to be a material that replicates a reference material as much 

as possible or to the degree specified. However, note that both materials may be simulants, which 

would allow one to compare two simulants to each other, or both may be actual lunar (or other 

material) samples, which would allow one to compare these materials to each other.

For engineering purposes, comparisons need to be based on defined, standardized measurements. Broadly speaking, one may subdivide possible measurements into either nominal or 

continuous functions. Nominal comparisons include such things as male versus female and apples 

versus oranges. Inherently, nominal characteristics do not recognize partial states. For example, a 

half apple-half orange is not generally physically meaningful terminology. Nominal designations 

are usually considered to be discrete functions. Continuous functions are those characteristics 

expressed using a real domain numbering system. For example, consider weight or length. For a 

real world particle, it is understood that there can, in principal, exist another particle that is arbitrarily close but not identical. The mathematics of comparing nominal and continuous functions 

is different.

2.2 Definition of Discrete Category Functions

A discrete category (DC) function is a function whose domain (i.e., input, independent variable, or argument) is a collection of discrete objects or categories all of the same kind and whose 

range (i.e., output, dependent variable or value of the function) is the quantity, fraction, or other 

value for each of the elements in the domain. Discrete category functions may be plotted as bar 

graphs. An example of a DC function is the composition of a material whose domain is the various 

constituents of the material and whose range is the various fractions of each constituent. A plot of 

such a function is shown in figure 1.
4

 

0.25

0.2

0.15

0.1

0.05

0

Fraction

Plagioclase

Olivine

Pyroxene

Spinel

Fe-Sulfide

Whitlockite

Ca-Phosphate

Ilmenite

Native Iron

Categories

Figure 1. Example discrete category function showing composition 

for a hypothetical material.

2.2.1 Definition of Reference and Simulant Category Value Vectors

A DC function relates its domain (input), which is a set of objects called categories, to its 

range (output), which is a set of values with one for each element of the domain. The domain and 

range may be collected into two vectors, one being a vector of categories and the other being a 

vector of values for those categories with a one-to-one correspondence between the elements of the 

two vectors. The vector of categories shall be called the category vector and the vector of category 

values the category value vector. Note that for category value vectors whose elements represent 

fractions of the categories, the sum of the elements of such a category value vector must necessarily sum to unity (the sum of the fractional parts must equal the whole). An example showing a 

composition category vector and category value vector is given in equation 1. The category vector 

is a vector whose elements are the various composition constituents of a material. The category 

value vector is a vector whose elements are the factions of the various constituents of the material 

as demonstrated in equation 1.

Category Vector Category ValueVector

plagioclase

olivine

nativeiron

.

.

.

































0.060

0.090 .

.

.

0.045































 (1)

2.2.2 Figure of Merit Computation

The FoM for a characteristic of a given reference and simulant material that is quantified 

by a DC function is defined as 1 minus the L1 norm of the weighted difference between a reference 

category value vector and a simulant category value vector scaled by the sum of the L1 norms of 
5

the weighted reference category value vector and the weighted simulant category value vector. This 

is shown in equation 2.

FoM = 1–

w cvvreference – cvv

simulant ( ) 1

wcvvreference

1

+ wcvv

simulant

1

= 1−

wi cvvi

reference – cvvisimulant ( )

i

∑

wicvvi

reference

i

∑ + wi

cvvi

simulant

i

∑ , (2)

where:

cvv is the category value vector of a material characteristic (reference material or simulant material).

w is a weighting vector (also referred to as the importance vector— consisting of 

a vector of weights). The weighting factor is used to specify the relative importance 

of particular elements of the category vector so that differences for certain categories may be made more important than others. This vector is an internal control for 

the FoM algorithm designers and developers and is a part of the FoM algorithm, 

so the user does not supply this vector.

vi is the ith element of vector v.

v 1 = v

i

i=1

n

∑ , is the L1 norm of vector v (also known as the taxi cab or Manhattan norm). (3)

2.3 Relative Frequency Distribution Functions

2.3.1 Definition of Relative Frequency Distribution Functions

The cumulative frequency distribution (CFD) (from which the relative frequency distribution (RFD) is derived) is defined and will be used in the FoMs that use an RFD for description 

of a material characteristic.

The CFD function CFDx(z) is defined as,

CFDx (z) = Fraction{x ≤ z} , (4)

which reads, CFDx(z) is the fraction of material characteristic x less than or equal to z. This is 

analogous to the probability cumulative distribution function Fx(z) that yields the probability that 

x is less than or equal to z. As an example, CFDsize(a) is the fraction of particles of size less than 

or equal to a.
6

 Interest will be in the derivative of the cumulative size frequency distribution function, 

which is defi ned as

RFDx (z) = d

dz

CFDx (z) . (5)

 This derivative is known as the RFD and yields the fraction of particles per particle material characteristic of material characteristic x. As an example, RFDsize(a) is the fraction of particles 

per particle size of size a. In concept, an RFD function is a function whose domain (i.e., input, 

independent variable, or argument) is a property of a material that varies discretely over some set 

of values (also known as bins) and whose range (i.e., output, dependent variable, or value of the 

function) is the quantity, fraction, or other value for bins in the domain. An RFD function may be 

plotted as a bar chart that shows the distribution by fraction of a given property of a material. As 

a bar chart, it consists of bars (which may be of varying widths) that are the bins for the quantity 

whose distribution is being described. The height of each bar represents the fraction of a given 

quantity over that bin.

 Examples of a size CFD function and its size RFD function are shown in fi gure 2.

1

0.8

0.6

0.4

0.2

0

Fraction

0 0.1 0.2 0.3 0.4

Size

0.1

0.08

0.06

0.04

0.02

0

Fraction

0 0.1 0.2 0.3 0.4

(a) (b) Size

Figure 2. Example cumulative (a) and relative (b) frequency distributions 

for particle size of a hypothetical material.

2.3.2 Figure of Merit for Relative Frequency Distribution Functions

 2.3.2.1 Defi nition of Discrete Data Relative Frequency Distribution. A relative frequency 

function may be defi ned as a continuous function (continuous domain or input) or a discrete function (discrete domain or input). However, for computational purposes, discrete data will be worked 

with, and the RFD is that histogram whose bars represent the fraction of particles within a given 

span of values for a given material characteristic such as size. The discrete RFD’s domain shall 

be defi ned by n+1 values that defi ne n contiguous bins with the value of each bin (height of the 

histogram bar) representing the fraction of particles between the lower and upper bin values, thus 
7

constituting the range of the RFD. There is no requirement for the bin sizes to be of the same size 

across the RFD, and variable bin sizes are allowed. Summation of the RFD range values between 

lower domain value zi and upper domain value zj yields the fraction of particles between zi and zj. 

Note that the summation of the entire RFD range (from minimum to the maximum domain value) 

must necessarily equal unity (the sum of the factional parts must equal the whole).

2.3.2.2 Figure of Merit Computation. For material characteristics quantified by an RFD, 

the FoM for how closely a simulant matches a reference is determined by comparing their RFD 

functions. The FoM for a characteristic of a given reference and simulant that is quantified by an 

RFD is defined as 1 minus the L1 norm of the weighted difference between a reference RFD and a 

simulant RFD scaled by the sum of the L1 norms of the weighted reference RFD and the weighted 

simulant RFD. This is shown in equation 6,

FoMbefore constrants = 1–

w RFDreference – RFDsimulant ( ) 1

wRFDreference

1

+ wRFDsimulant

1

= 1– w∫ RFDreference – RFDsimulant

w RFDreference ∫ + w RFDsimulant ∫

= 1−

wi RFDi

reference – RFDisimulant ( )widthi

i

∑

wiRFDi

referencewidthi

i

∑ + wi

RFDi

simulant

widthi

i

∑ , (6)

where,

RFD = the RFD function of a material characteristic (reference material 

or simulant material)

w = a weighting function (also referred to as the importance function) that is 

used to specify the relative importance of various regions of the RFD function domain (input of RFD function) to each other, so that RFD differences 

for certain regions may be made more important than others. This function 

is an internal control for the FoM algorithm designers and developers and 

is part of the FoM algorithm, so the user does not supply this function.

vi = the value of a function over the ith bin when a function is discretized over 

a number of bins (the domain of the RFD function is discretized into discrete bins).

v(x) 1 = v(x) dx ∫ , = the L1 norm of a function v(x). (7)
8

widthi = the width of the ith bin, which when multiplied by vi, the value of the 

function v over the ith bin, yields the integral of the of the function over 

the ith bin.

The FoM just described is further subject to certain maximum error constraints as identified 

in equation 8,

FoM =

0 otherwise

FoMbefore constraints if RFDreference −RFDsimulant ≤maxRFDdifference ⎧

⎨

⎪

⎩⎪

. (8)

The quantity max RFDdifference is an internal control for the FoM algorithm designers and 

developers and is a part of the FoM algorithm; therefore, the user does not supply this quantity.
9

3. FIGURE OF MERIT DESCRIPTIONS

3.1 Modal Composition

Modal composition defines the geologic constituents of a simulant without reference to textural features such as particle shape and particle size. The FoM algorithm for modal composition 

treats composition as a vector of the fractions of the various constituents of the material, which 

may be viewed as a DC function and plotted as a bar graph of the various constituents. Modal 

composition is further subdivided into mineral composition and a broader FoM termed general 

composition that includes minerals and the top level categories Lithic Fragments, Glasses, Agglutinates, and Other (nonlunar materials and contaminants). In both cases, the FoM is defined as the 

scaled L1 Norm of the difference of two composition vectors subtracted from unity. The L1 Norm 

(also known as the taxi cab or Manhattan norm) is defined as the sum of the absolute values of the 

components of a vector (see equation 9).

v 1:= vi

i=1

n

∑ . (9)

The FoM for modal composition may be interpreted as the fraction of material that is the 

same in both materials and is computed as described in section 2.2.1.

3.2 Particle Size Distribution

Size distribution refers to the distribution of particle sizes within a material. Size distribution is naturally represented by an RFD that may be plotted as a histogram of the fraction of 

particles within a given size range. The FoM is defined as the scaled L1 Norm of the difference of 

two RFDs subtracted from unity. The FoM for size distribution may be interpreted as the fraction 

of particles sizes that both materials have in common and is computed as described in section 2.3.2.

3.3 Particle Shape Distribution

Shape Distribution refers to the distribution of particle shapes within a material. Two shape 

characteristics have been defined. These are the aspect ratio of the grains of the material and the 

angularity of the grains of the material. In general, the particles in a material will exhibit a range 

of aspect ratios and a range of angularities. Thus, the FoMs for aspect ratio and angularity are 

based on the RFD of aspect ratio and angularity respectively. However, realizing that distributional data on aspect ratio and angularity may be difficult to obtain, a provision has been made 

for computing an alternate FoM based on the mean aspect ratio and the mean angularity over the 

ensemble of particles.
10

When distributional data are available, the FoMs for aspect ratio and angularity are defined 

as the scaled L1 Norm of the difference of two RFDs subtracted from unity. The FoMs for aspect 

ratio and angularity are computed as described in section 2.3.2. The FoMs for shape may be interpreted as the fraction of particle shapes that both materials have in common.

When only mean data is available, the FoMs for aspect ratio and angularity are computed 

as described in section 2.2.1. The FoMs for shape in this case may be interpreted abstractly as the 

amount of shape that the two materials have in common.

When only mean data is available, the FoMs for aspect ratio and angularity are defined 

as the scaled absolute value of the difference of the two means subtracted from unity. In this case, 

computations are performed as described in section 2.2.1. The FoMs for shape in this case may 

be interpreted abstractly as the amount of aspect ratio or angularity that the two materials have 

in common.

3.4 Density

Density refers to weight per unit volume of a material; however, for divided solids consisting of a collection of particles, the volume of a material will necessarily consist of particle volume, 

interparticle void volume, and internal pore volume. Therefore, density is defined to refer to bulk 

density and require any density measurements to be made over a sample sufficiently large enough 

so that the sample follows the particle size distribution of the material. Because bulk density is not 

an intrinsic property of a material but depends in part on how a material is handled, the FoM for 

density is defined to include a minimum bulk density, a maximum bulk density, and the specific 

gravity of the material, where specific gravity is the ratio of particle density to the density of water.

Bulk densities and the specific gravity may be treated as elements of a density vector, which 

may be viewed as a DC function and plotted as a bar graph of the various kinds of density. The 

FoM for density is defined as the scaled L1 Norm of the difference of two density vectors subtracted from unity. The FoM for density is computed as described in section 2.2.1 and may be interpreted abstractly as the amount of density the two materials have in common.
11

4. SOFTWARE DESCRIPTION

The FoM software implements six FoM algorithms to evaluate how well a lunar regolith 

simulant compares to a reference material.

The software consists of the following three components:

(1) An input editor. Microsoft Excel® software is used for this purpose.

(2) A back end that computes the FoMs. Code developed with the MathWorks MATLAB®

software is used for this purpose.

(3) A front end with which the user interacts that opens and reads the Excel input files, performs 

checks on the inputs, and calls the MATLAB routines for computation of the FoMs. This is 

custom code created with the LabWindows/C for Virtual Instrumentation (CVI) software from 

National Instruments.

These base components were chosen because they are sold world wide (minimizing potential International Traffic in Arms Regulations (ITAR) and other legal complications), are relatively 

inexpensive, their use greatly reduces costs to the simulant development program, and they simplify 

licensing problems

4.1 Software Inputs

Input to the software consists of six spreadsheet tables that tabulate the composition, size 

distribution, shape, and density of a simulant material and the reference material to which it is 

being compared. Portions of the input for computation of the Modal Composition—Minerals 

FoM, Modal Composition—General FoM, Size Distribution FoM, Shape—Aspect Ratio FoM, 

Shape—Angularity FoM, and Density FoM are presented in section 5.
12

5. DATA ENTRY FOR THE FIGURE OF MERIT SOFTWARE

5.1 Introduction

Reference and simulant data are stored in a specific format in Excel data files. The data files 

must be formatted per the FoM Template.xlt file. This read-only file is automatically placed in the 

\FoMData folder under the root directory (nominally c:) on the Windows volume of the computer 

during installation of the FoM software. Reference material and simulant material data files are 

identical.

5.2 Structure of the Data Files

The FoM template workbook contains seven worksheets as described in the following paragraphs. The workbook is protected to prevent moving, adding, or deleting worksheets. Each worksheet is protected to prevent modification of any field except data entry fields. The worksheets are 

color coded to designate data entry fields, computation fields, and help fields.

Data entry fields are highlighted with a yellow background color and a red border. These 

fields are the only fields in which the user can enter data. Figure 3 shows an example of a blank 

data field.

Figure 3. Example data entry field.

Data validation is provided as much as possible to help the user enter data completely and 

correctly. For example, on the Size Distribution sheet, checks are performed on size ranges to verify 

that the sizes are in ascending order.

Fields with light-green shading indicate cells that are computed; that is, they compute a 

value based on data that the user has entered. These cells are included for error checking and to aid 

the user in data entry. As an example, the elements of a composition vector must necessarily sum 

to unity (the sum of the fractional parts must equal the whole). To help the user in entering data, 

summation fields are provided that sum up the elements of a composition vector and contain an 

error message if a set of data entry fields does not sum to unity as required. An example from the 

Modal Composition—General worksheet (showing columns for Size Range 1 and Size Range 2) 

is shown in figure 4.

Figure 4. Example computation field.
13

Fields with help are labeled with blue, underlined text. Moving the mouse over blue, underlined text will cause an input tip to appear. Each data input worksheet also has a blue outlined box 

with short instructions unique to that page. Figure 5 shows an example.

Figure 5. Example help.

Certain fields obtain their values from other fields on the same or other worksheets via links. 

These fields are shown in gray. An example of a linked field is on the Modal Composition—General worksheet that contains data from the Modal Composition—Minerals worksheet under the 

category Mineral Grains. Figure 6 shows an example of a linked field in gray.

Figure 6. Example linked data field.

5.3 Worksheet Def﻿initions

5.3.1 Description Worksheet

This worksheet contains version control information for the template file and has a notes 

field in which the user may enter notes for this workbook. This sheet is for documentation purposes 

only and is not used by the FoM software. It is shown in figure 7.

5.3.1.1 Specific Instructions. Step 1: Notes for the workbook may be entered in the block 

titled Notes.

5.3.2 Modal Composition—Minerals Worksheet

This worksheet is used to enter modal composition data for minerals. Modal composition 

is specified by the fraction of each constituent in a material for a given particle size range. If a component is not present in a sample, the fraction field should be filled with zero or may be left blank.
14

Figure 7. Description worksheet.

Certain minerals are actually solid solutions of various compounds. These are best handled 

by providing the mean fraction of the solution components as subcategories. For example, 

consider that a plagioclase consisting of a mixture of 60% albite (NaAlSi3O8) and 40% anorthite 

(CaAl2Si2O8) may be classified as andesine, and a plagioclase consisting of a mixture of 50% albite 

and 50% anorthite may be classified as labradorite. If these were so labeled, the FoM algorithm 

would consider these to be separate unrelated minerals even though they are fairly similar, as the 

algorithm does not understand mineral composition. By specifying the underlying compounds in 

the solution, this problem is avoided and an accurate comparison may be made.

For the solid solutions, a second level of constituents is specified, namely the fractions of 

the compounds that make up the solution.

Level 1 contains a list of nine minerals (plagioclase, olivine, pyroxene, spinel, iron (Fe) 

sulfide, whitlockite, apatite, ilmenite, and native Fe). As of now, whitlockite and apatite cannot be 

separately distinguished because both are similar calcium (Ca) phosphates; however, it is hoped 

that a differentiation can be made in the future. Therefore, a placeholder for whitlockite is provided 

but is currently not used. All Ca phosphates should be entered under apatite. Of the level 1 components, four are solid solutions (plagioclase, olivine, pyroxene, and spinel), whose constituents may 

be further specified at level 2. Figure 8 shows this hierarchical arrangement on the Modal Composition—Minerals worksheet.
15

Figure 8. Modal Composition—Minerals worksheet.

The level of detail need not be uniform across the various levels, nor must it match the other 

material being compared. Note that the fractions at level 1 must necessarily sum to unity (the sum 

of the fractional parts must equal the whole), and the children of a level 1 item must also sum to 

unity. Thus, the fractions at level 2 represent the fractions of the parent.

If no information is available at a sublevel when entering data, then a rolled up value may be 

supplied one level higher up. Since currently there are only two levels, this means that data may be 

supplied just at level 1 if no data is available at level 2. More detail is presented in section 5.3.2.1.

Modal composition data may be entered as a function of particle size for up to eight size 

ranges. The FoM software computes a separate Modal Composition—Minerals FoM for each size 

range in which both the reference and simulant data files contain data. The data in corresponding 

size ranges is used to compute the FoM. As composition may be a function of size, care should be 

taken to compare data containing closely matching size ranges to ensure an accurate comparison. 

Since an FoM is computed for each size range, size ranges are not required to be contiguous and 

may even overlap.

5.3.2.1 Specific Instructions. The following steps are specific instructions for entering data.

Step 1: Enter the particle size range lower and upper limits into the cells in the row labeled Size, 

under the heading Size Range i for the ith size range set of data.
16

Note: If compositional data is not a function of size or if the particles span all sizes, then 

the size fields may be left blank. This data is currently not used for any computations and 

is for informational purposes only. However, it may be used in the future.

Step 2: Enter the units for the sizes in the fields below the size fields in the row labeled Units.

Note: Both the sizes (lower size limit and upper size limit) must be in the same units.

Note: This field features a drop-down menu from which the μm, mm, and cm units may 

be selected. This data is currently not used for any computations and is for informational 

purposes only. However, it may be used in the future.

Step 3: For the size ranges defined in steps 1 and 2, enter the mineral modal compositional fractions of the material in the column under the heading Fraction Level 1. Note that there 

are eight categories of modal composition at this first level (plagioclase, olivine, pyroxene, 

spinel, Fe sulfide, apatite, ilmenite, and native Fe).

Step 4: For the size ranges defined in steps 1 and 2 and for the level 1 items that have children 

(plagioclase, olivine, pyroxene, and spinel), enter the modal compositional fractions of the 

constituent minerals of the parent in the column under the heading Fraction Level 2 if 

they are known. If they are not known, then leave blank.

Note: As constituent fractions are entered, they are totaled in the light green computation 

fields of the worksheet for the material as a whole and for the four level 1 constituents that 

have children. This aids in data entry, as one of the requirements is that the fractions must 

sum to unity.

Step 5: Notes for the worksheet may be entered in the block titled Notes.

5.3.2.2 Example. In the example shown in figure 9 for Size Range 1, it is known that the 

mineral composition for plagioclase, olivine, pyroxene, spinel, Fe sulfide, apatite, ilmenite, and 

native Fe is 24%, 30%, 18%, 15%, 5%, 6%, 0%, and 2%, respectively. Further, the composition of 

the solid solution plagioclase is 35% albite and 65% anorthite. The composition of the solid solution pyroxene is 72% clinopyroxene and 28% orthopyroxene. No further information is available 

on the composition of the olivine or spinel. 

5.3.3 Modal Composition—General Worksheet

This worksheet is used to enter modal compositional data for minerals and other constituents. Modal composition is specified by the fraction of each constituent in a material for a given 

particle size range. If a component is not present in a sample, the fraction field should be filled with 

zero or may be left blank.

Data may be specified at various levels of detail. Presently, there are three levels of categories. The first level consists of four categories of materials (Lithic Fragments, Mineral Grains, 

Glasses, and Agglutinates) and, for simulant materials only, Other (lunar regolith by definition 
17

Figure 9. Modal Composition—Minerals example.

does not contain nonlunar materials or contaminants). The second and third levels are further 

decompositions of levels 1 and 2, respectively, into components as shown in the Modal Composition—General Worksheet, figure 10. The level of detail need not be uniform across the various 

categories and subcategories, nor must it match the other material being compared.

When entering data, if no information is available at a sublevel, then a rolled-up value may 

be supplied one level higher. More detail is presented in section 5.3.3.1. 

The fields for Mineral Grains and Size Ranges show up as gray, indicating that data cannot be entered into them. Rather, the data in these fields are linked to the data that were previously 

entered into the worksheet Modal Composition—Minerals, since the constituents and size ranges 

are the same.

On the Modal Composition—Minerals worksheet, level two items that were siblings (have 

the same parent) summed to unity. However, on the Modal Composition—General worksheet, all 

fractions are fractions of the total, not the parent; therefore, all fractions must sum to unity.
18

Figure 10. Modal Composition—General worksheet.

Modal composition data may be entered as a function of particle size for up to eight size 

ranges. The FoM software computes a separate modal composition FoM for each size range in 

which both the reference and simulant data files contain data. The data in corresponding size 

ranges is used to compute the FoM. As mentioned previously, size range data on the Modal Composition—General worksheet are linked to the size range data on the Modal Composition—Minerals worksheet; therefore, these data need not and cannot be entered on this worksheet.

5.3.3.1 Specific Instructions. The following steps are specific instructions for entering data.

Step 1: For the size ranges previously defined, enter the modal compositional fractions of the 

constituents in the material in the column under the heading fraction. Note that there are 

five subdivisions of modal composition at the first level, Lithic Fragments, Mineral Grains, 

Glasses, Agglutinates, and Other.

If one or more level 1 constituents cannot be further subdivided (i.e., if data is unavailable 

at a lower level), the fraction of material at this level is entered in the field labeled ‘enter roll up or 

break down’ (see figure 10). This is also known as entering a rolled-up value for the level below. 

Otherwise, if fractional data is available at a lower level, leave this field blank and enter the fractions for the appropriate constituents at the lower level.

Note: Fractions should only be entered in the field labeled ‘enter roll up or break down’ (see 

figure 10) or in the fields below this field.
19

Note: As constituent fractions and data for the material as a whole are entered, they are 

subtotaled at the next higher level in the light green computation fields of the worksheet. 

This aids in data entry, as one of the requirements is that the fractions must sum to unity.

Step 2: For Glasses, enter a descriptor for the kind of glass.

Note: The descriptor for kind of glass must match between the reference material and the 

simulant material and must be in the same row for both materials.

Step 3: For Agglutinates, enter a descriptor for the kind of agglutinate.

Note: The descriptor for kind of agglutinate must match between the reference material 

and the simulant material and must be in the same row for both materials.

Step 4: A category labeled Other exists for simulant material worksheets only, which may be used 

to enter fractions for unknown (nonlunar materials) constituents and for contaminants.

Note: Lunar regolith by definition does not contain nonlunar materials or contaminants, 

and so must have a zero value for Other.

Step 5: Notes for the worksheet may be entered in the block titled Notes.

5.3.3.2 Example. In this example, shown in figure 11, it is known that 58% of a material in 

the first size range is made up of lithic fragments; however, no further breakdown is known. Therefore, 0.58 is entered on the line labeled Lithic Fragments in the field labeled ‘enter roll up or break 

down’ (see figure 11). Mineral data were previously entered in the worksheet Modal Composition—

Minerals; therefore, only the fraction of mineral grains in the material needs to be entered. This is 

known to be 24%. Finally, it is known that the remaining composition consists of 8% green glass, 

6% brown glass, 1% agglutinates (no further breakdown available), and 1% nonlunar materials and 

contaminants, which consist of 0.5% hydrous/carbonated material and 1.5% nonlunar abrasive 

material. Figure 11 shows Size Range 1.

5.3.4 Size Distribution Worksheet

This worksheet is used to enter the size distribution data. Size distribution is specified as 

an RFD histogram by the fraction of the material that falls within a specified size bin. If the data 

are not in RFD form, then they must first be converted to this form (see section 3.2). The fractions 

within all specified bins must sum to unity. A value of zero is the default if no fraction is entered. 

Figure 12 shows the Size Distribution worksheet.

Bin sizes for the size distribution must be contiguous, and bins must be specified in order of 

ascending size. The user enters the upper bin size with units for a given bin size. For the lower bin 

size, the FoM software uses the previous bin’s upper bin size; therefore, for the first bin, a lower bin 

size and units must also be specified.
20

Figure 11. Modal Composition—General example.
21

Figure 12. Size Distribution worksheet.

5.3.4.1 Specific Instructions. Size distribution is specified as an RFD histogram. If the data 

are not in RFD form, they must first be converted to this form.

Step 1: Enter the units for the lower and upper bin size for the first bin in the column labeled Bin 

Size Units. Units must be μm, mm, or cm. The units are used to scale all size data to a consistent set of units since size data may be entered in different units in different bins. Continue to enter the units for the upper bin size for the second and succeeding bins until units 

have been entered for every bin for which data exists.

Note: The Bin Size Units cells feature a drop down menu from which the μm, mm, and cm 

unit may be selected.

Step 2: Enter the lower and upper bin size for the first bin in the column labeled Bin Sizes. Continue 

to enter upper bin sizes for the second and succeeding bins until upper bin sizes have been 

entered for every bin for which data exists.

Note: Lower bin sizes for bins other than the first bin are obtained from the upper bin sizes 

of the preceding bins.

Step 3: Enter the fraction of particles that fall within the first size bin in the column labeled Fraction. Fraction must be a number between zero and 1. Continue to enter fractions for the 

second and succeeding size bins until fractions have been entered for every bin for which 

data exists.
22

Note: The fractions for all bins must sum to unity.

Step 4. Notes for the worksheet may be entered in the block titled Notes.

5.3.4.2 Example. In the example shown in figure 13, size fractions for 12 size bins are 

known. For Bin 1, the lower and upper bin size units and bin sizes must be specified; for all other 

bins, only the upper bin size needs to be specified.

Figure 13. Size Distribution example.

5.3.5 Shape—Aspect Ratio Worksheet

This worksheet is one of two for entering particle shape data. In particular, this worksheet 

allows entry of particle aspect ratio data. Particle aspect ratio is nominally specified as an RFD 

histogram by the fraction of material whose aspect ratios fall within a specified aspect ratio shape 

bin. The fractions within all specified bins must sum to unity. A value of zero is the default if no 

fraction is entered.

If RFD data for aspect ratio is provided, then the mean aspect ratio is computed. However, 

if the aspect ratio distribution is unknown, it may be replaced by the scalar mean aspect ratio over 

all the particles in the material. In this case, the user enters the mean aspect ratio into the field that 

would contain the computed mean aspect ratio had the data for the RFD been available. Figure 14 

shows this worksheet.
23

Figure 14. Shape—Aspect Ratio worksheet.

Since aspect ratio is a ratio of two values, it is a dimensionless quantity and units are not 

specified. Bin values for the aspect ratio distribution must be contiguous. Also, bins must be specified in order of increasing aspect ratio. The user enters the upper bin value for a given bin. This 

value also becomes the lower bin value for the next bin. For the first bin, a lower and upper bin 

value must be specified.

5.3.5.1 Specific Instructions. Aspect ratio distribution is specified as an RFD histogram. 

If the data are not in RFD form, then they must first be converted to this form.

Step 1: Enter the particle size range lower and upper limits into the cells in the row labeled Size, 

under the heading Size Range i for the ith size range set of data.

Note: If aspect ratio data is not a function of size, or if the particles span all sizes, then the 

size fields may be left blank. This data is currently not used for any computations and is for 

informational purposes only; however, it may be used in the future.

Step 2: Enter the units for the sizes in the fields below the size fields in the row labeled Units.

Note: Both the sizes (lower size limit and upper size limit) must be in the same units.
24

Note: This field features a drop-down menu from which the μm, mm, and cm units may be 

selected. This data is currently not used for any computations and is for informational purposes only; however, it may be used in the future.

Step 3: For the size ranges defined in steps 1 and 2, enter the lower and upper bin aspect ratio values for the first bin in the column labeled Aspect Ratio. Continue to enter upper bin aspect 

ratio values for the second and succeeding bins until upper bin aspect ratio values have been 

entered for every bin for which data exists.

Note: Lower bin aspect ratio values for bins other than the first bin are obtained from the 

upper bin aspect ratio values of the preceding bins.

Step 4: Enter the fraction of particles whose aspect ratios fall within the first aspect ratio bin in the 

column labeled Fraction. Fraction must be a number between zero and 1. Continue to enter 

fractions for the second and succeeding aspect ratio bins until fractions have been entered 

for every bin for which data exists.

Note: The fractions for all bins must sum to unity.

Step 5.If the aspect ratio distribution is unknown, the user may enter just the mean aspect ratio 

into the field labeled Mean Aspect Ratio. If aspect ratio distribution data is known, it is 

used to compute the Mean Aspect Ratio.

Note: Do not enter both RFD aspect ratio data and mean aspect ratio data.

Step 6:Notes for the worksheet may be entered in the block titled Notes.

5.3.5.2 Example. In this example, shown in figure 15, aspect ratio fractions for five aspect 

ratio bins are known. For Bin 1, the lower and upper bin aspect ratios must be specified; for all 

other bins, only the upper bin aspect ratio needs to be specified.

5.3.6 Shape—Angularity Worksheet

This worksheet is the second of two for entering particle shape data. In particular, this 

worksheet allows entry of particle angularity data. Particle angularity is nominally specified as an 

RFD histogram by the fraction of material whose angularities fall within a specified angularity 

shape bin. The fractions within all specified bins must sum to unity. A value of zero is the default 

if no fraction is entered.

If RFD data for angularity is provided, the mean angularity is computed. However, if the 

angularity distribution is unknown, it may be replaced by the scalar mean angularity over all the 

particles in the material. In this case, the user enters the mean angularity into the field that would 

contain the computed mean angularity had the data for the RFD been available. Figure 16 shows 

the Shape—Angularity worksheet.
25

Figure 15. Shape—Aspect Ratio example.

Figure 16. Shape—Angularity worksheet.
26

Bin values for the angularity distribution must be contiguous. Also, bins must be specified in 

order of increasing angularity. The user enters the upper bin value for a given bin. This value also 

becomes the lower bin value for the next bin. A lower and upper bin value must be specified for the 

first bin.

5.3.6.1 Specific Instructions Angularity distribution is specified as an RFD histogram. 

If the data are not in RFD form, they must first be converted to this form.

Step 1: Enter the particle size range lower and upper limits into the cells in the row labeled Size, 

under the heading Size Range i for the ith size range set of data.

Note: If angularity data is not a function of size, or if the particles span all sizes, then the 

size fields may be left blank. This data is currently not used for any computations and is for 

informational purposes only; however, it may be used in the future.

Step 2: Enter the units for the sizes in the fields below the size fields in the row labeled Units.

Note: Both the sizes (lower size limit and upper size limit) must be in the same units.

Note: This field features a drop down menu from which the μm, mm, and cm units may be 

selected. This data is currently not used for any computations and is for informational purposes only; however, it may be used in the future.

Step 3: For the size ranges defined in steps 1 and 2, enter the lower and upper bin angularity values 

for the first bin in the column labeled Angularity. Continue to enter upper bin angularity

values for the second and succeeding bins until upper bin angularity values have been 

entered for every bin for which data exists.

Note: Lower bin angularity values for bins other than the first are obtained from the upper 

bin angularity values of the preceding bins.

Step 4: Enter the fraction of particles whose angularities fall within the first angularity bin in the 

column labeled Fraction. Fraction must be a number between zero and 1. Continue to enter 

fractions for the second and succeeding angularity bins until fractions have been entered for 

every bin for which data exists.

Note: The fractions for all bins must sum to unity.

Step 5:If the angularity distribution is unknown, the user may enter just the mean angularity into 

the field labeled Mean Angularity. If angularity distribution data is known, it is used to 

compute Mean Angularity.

Note: Do not enter both RFD angularity data and mean angularity data.

Step 6: Notes for the worksheet may be entered in the block titled Notes.
27

5.3.6.2 Example. In this example, shown in figure 17, the angularity distribution is 

unknown. However, a mean angularity of 28.3 has been determined. Therefore, the user enters 

the mean value into the field labeled Mean Angularity.

Figure 17. Shape—Angularity example.

5.3.7 Density Worksheet

This worksheet is used to enter the density data. Density is the ratio of the material’s mass 

to volume. However, because the materials being compared are particulate, various volumes may 

be considered in the definition including volume with or without interparticle void volume and 

internal pore volume. As a result, three different measures of density (i.e., mean specific gravity, 

minimum bulk density, and maximum bulk density) are defined. Precise definitions of these terms 

may be found in reference 1. These are entered into the Density worksheet shown in figure 18.

5.3.7.1 Specific Instructions. 

Step 1: Enter the mean specific gravity of the material into the field labeled Mean Specific Gravity. 

Since this is a ratio, it is a dimensionless quantity and has no units.

Step 2: Enter the minimum bulk density of the material into the field labeled Minimum Bulk 

Density.

Step 3: Enter the units for minimum bulk density into the field labeled Units under Minimum Bulk 

Density. Note that units must be either g/cm3 or kg/m3.

Step 4: Enter the maximum bulk density of the material into the field labeled Maximum Bulk 

Density.
28

Figure 18. Density worksheet.

Step 5: Enter the units for maximum bulk density into the field labeled Units under Maximum Bulk 

Density. Note that units must be either g/cm3 or kg/m3.

Note: The Units cell features a drop-down menu from which the g/cm3 or kg/m3 units may 

be selected.

Step 6: Notes for the worksheet may be entered in the block titled Notes.

5.3.7.2 Example. In this example, shown in figure 19, the mean specific gravity of a 

material is 2.345, the minimum bulk density is 2.102 g/cm3 and the maximum bulk density 

is 2.789 g/cm3.

5.4 Creating a Reference or Simulant Data File

Once data for a reference and simulant material is collected, it must be entered into an Excel 

file with the exact structure as the FoM Template.xlt file installed with the FoM software. The steps 

for creating a reference or simulant data file are identical; therefore, this section will refer to either 

file as the sample data file.

Note: The following steps show two different methods for creating a sample data file. Either 

method may be used but both methods should not be used simultaneously.
29

Figure 19. Density example.

Note: The c:\ in the pathnames represents the Windows’ volume. The user may need to use a 

different drive designator if the Windows’ volume on your computer is not c:\.

Step 1: Create an empty sample data file from the FoM Template.xlt in the default FoM data folder 

using one of the following methods:

• Method 1: Directly from an Excel application:

– Open the c:\FoMData\FoM Template.xlt with an Excel file by double-clicking the file or using

 the File>>Open menu item from within Excel.

– Use the File>>Save As... menu item from within Excel to save the template in a new file.

 • Double click the folder or use the Save in line of the Save As dialog box to specify where the

 file should be saved.

 • Use the File name line in the dialog box to specify the sample data file name.

 • Click the Save button in the dialog box. This will save an empty sample data file without the 

 read-only attribute that the FoM Template.xlt file has.

• Method 2: From within the FoM application:

– Open the FoM application from the Start>>All Programs>>Figures of Merit list item.

– From within the FoM application, select the File>>New... menu item.

 • Double click the folder or use the Save in line of the dialog box to specify where the file

 should be saved.

 • Use the File name line in the dialog box to specify the sample data file name.

 • Click the Save button in the dialog box. This will save an empty sample data file without the

 read-only attribute that the FoM Template.xlt file has. A confirmation dialog box will appear 

 stating that a new sample data file has been created.

Step 2: Edit and save the sample data file using one of the following methods:

• Method 1: Directly from an Excel application:

– Open the newly created sample data file with an Excel file by double-clicking the file or using 

 the File>>Open menu item from within Excel.
30

– Enter data in the yellow highlighted fields.

– Use the File>>Save menu item from within Excel to save the entered data.

• Method 2: From within the FoM application:

– From within the FoM application, select the File>>Open>>Reference or 

 File>>Open>>Simulant menu item, depending on whether the file should be interpreted as 

 reference material or simulant material.

• Double click the new sample data file or type the name into the File name line in the dialog 

box. Excel will be launched and the selected file will appear. If the selected data file does 

not appear, you may need to click the Excel button on the task bar to bring the window 

to the front.

– Use the File>>Save menu item from within Excel to save the entered data.

– As an alternative, use the File>>Close>>Reference or File>>Close>>Simulant menu item in 

the FoM application. The user will be asked to confirm saving the data before the file is closed.
31

6. USING THE FREQUENCY OF MERIT SOFTWARE

6.1 Selecting Reference and Simulant Data Files for Figure of Merit Calculations

Both a reference and a simulant data file must be selected prior to performing any FoM 

calculations. Any Excel data file adhering to the exact format of the FoM Template.xlt file may be 

used as a reference or a simulant data file; therefore, a file that was originally created as a simulant 

may be selected as a reference if the user desires to compare two simulants.

When the FoM software is first opened, no reference or simulant data is selected. The fields 

titled Reference and Simulant, as shown in figure 20, on the main window of the FoM software 

indicate this.

Figure 20. Reference and Simulant data file selection fields.

Once a reference and/or simulant data file is selected, it can only be unselected by selecting 

another file or exiting the FoM software. The None Selected appears in these fields only until a file 

is selected for the first time.

There are two ways to select a Reference or Simulant data file; both are from within the 

FoM software.

Method 1: Select and open the data file for viewing as follows:

• Select the File>>Open>>Reference or File>>Open>>Simulant menu item. A file select dialog 

box will appear.

• Double click the desired sample data file or type the name into the File name line in the dialog 

box. Excel will be launched and the selected file will appear. If the selected data file does not 

appear, the user may need to click the Excel button on the task bar to bring the window to the 

front.
32

• The selected data file name will appear in the box under Reference or Simulant in the main FoM 

window.

Method 2: Select the data file, but do not open for immediate viewing as follows:

• Move the mouse cursor over the label Reference or Simulant that appears on the main window 

of the FoM software. When the word becomes a highlighted yellow color, click the mouse once 

as shown in figure 21. A file select dialog box will appear.

Figure 21. Selection of a reference material data file.

• Double click the desired sample data file or type the name into the File name line in the dialog 

 box. Excel will be launched and the selected file will open but will be minimized as a button on 

 the task bar.

• The selected data file name will appear in the box under Reference or Simulant in the main FoM 

 window as shown in figure 22.

Figure 22. Filled in fields for reference and simulant material data files.

After both a reference and simulant data file have been selected, the FoM calculation functions may be executed.

6.2 Computing Figures of Merit

6.2.1 Introduction

Once the input data files for the FoM software have been opened, computation of the FoMs 

may proceed. In addition to the data about the reference material and the simulant material, the 
33

user must supply various other inputs. One of these has already been described, namely the Importance Vector for Modal Composition and the Importance Weighting Function for Size Distribution. 

Although not an intrinsic property of the reference material, Importance was included in the reference material workbook for convenience since the Importance has the same dimensions as, and must 

match, the data that it weighs. This made data entry a little easier than requiring a third workbook 

or prompting the user for the data in the application proper. Other inputs that the user must supply 

are described in the FoM sections where the input is appropriate. FoM computation may be initiated 

by one of two methods.

Method 1: Using the Window menu, select the Window>>FoM>> and then one of the following menu items: The Modal Composition, Size Distribution, Shape, or Density. 

Method 2: Selecting the desired FoM computation in the main application window, move the 

mouse cursor over the FoM that you wish to compute that appears on the main window of the FoM 

software. Modal Composition and Shape have a second tier of choices that may be selected by moving the cursor first over Modal Composition or Shape and then over the second tier to be selected. 

When the word becomes a highlighted yellow color, as shown in figure 23, click the mouse once. The 

example in section 6.2.2 shows how to initiate a Modal Composition—General computation.

Figure 23. Color change indicating a selection.

Either method will result in a dialog box appearing that will allow further option selection. 

The specific details for each FoM follow.

6.2.2 Modal Composition—Minerals

Selection of the Modal Composition—Minerals FoM computation causes the Modal Composition FoM—Minerals dialog box, shown in figure 24, to appear.

Pressing the Close button closes the dialog box and terminates FoM computation.

Pressing the Start Calculation button initiates computation of up to eight different modal 

composition FoMs corresponding to the eight different size ranges on the Modal Composition—

Minerals worksheet in which data may have been provided.
34

Figure 24. Modal Composition—Minerals FoM dialog box.

The dialog box also allows the user to suppress a ‘Size Range Mis-match’ warning. If ‘Size 

Range Mis-match’ warnings are not suppressed, then a warning results when a given size range 

in the reference material worksheet does not match the corresponding size range in the simulant 

worksheet. The purpose of this warning is to alert the user to the fact that data for inconsistent size 

ranges are being compared. While small mismatches may not matter, large ones may be indicative 

of a data entry error. The warning appears as shown in figure 25.

Figure 25. Size Range Mis-match warning dialog box.

Selecting Yes allows the FoM computation to proceed. Selecting No terminates the calculation for that size range.

If ‘Size Range Mis-match’ warnings are suppressed, then size range mismatches are ignored 

and the FoMs will be computed for all size ranges for which data exists in both the reference and 

simulant data files.
35

Composition fractions for modal composition are required to sum to unity. In practice 

however, fractions may not sum to exactly unity because of numerical round off. Therefore, a band 

has been defined around unity that is considered unity for summing purposes. Thus, sums that fall 

within the range 1 ± Band are considered to be 1. The default value for Band is 0.001 so that all 

sums between 0.999 and 1.001 are considered to be 1. The value of Band may be set to different 

values if the default is not appropriate.

Checking the box labeled Plot under each size range will produce a set of bar graphs that 

show the reference fractional modal composition, the simulant fractional modal composition as 

separate plots, the reference and simulant fractional modal composition in a combined plot, and 

the difference of the reference and simulant fractional modal composition. These plots are provided as visual aids to the FoM computation. Examples are shown in figures 26 and 27.

Figure 26. Modal Composition—Minerals reference and simulant bar graphs.
36

Figure 27. Modal Composition—Minerals joint and difference bar graphs.

Finally, pressing the View Tree button brings up the Modal Composition Tree—Minerals window. This window, shown in figure 28, shows the modal compositional data in hierarchical 

view for each size range. The user may select to view the various fractions as fractions of the whole 

(Fraction of Total) or as fractions of the parents at a particular level (Fraction of Level).

The refresh button will initiate a reread of the Modal Composition—Minerals Excel worksheet. If the tree window is open when the user edits the worksheet, the software should detect the 

change and automatically close the tree window. Whenever the tree window is opened, it checks 

to see if the worksheet has been changed since the last read. If it has been changed, the file will be 

reread. The refresh button forces a new read of the worksheet even if the software thinks the file 

has not changed since the last read. Under nominal conditions, this button should never have to 

be used; however, it may be used if, for any reason, the user believes that the latest updates to the 

worksheet have not been loaded into the tree window.
37

Figure 28. Modal Composition—Minerals data tree view.
38

6.2.2.1 Window Menu. The Window menu contains the following menu items 

(see figure 29):

• Print: Opens the standard dialog box for printing files to print the tree window.

• Close: Closes the tree window.

Figure 29. Window menu.

The user may also right click in the tree window, which brings up a control menu shown in 

figure 30 from which the user can perform a search (Find), expand or collapse the entire tree or a 

subset thereof (this can also be performed with the ± icons), and can change the font size. Font size 

changes are remembered so the user can set and forget them.

Figure 30. Modal Composition—Minerals tree control menu.

Pressing the Close button (not shown) closes the window.

6.2.3 Modal Composition—General

Selection of the Modal Composition—General FoM computation causes the Modal Composition FoM—General dialog box shown in figure 31 to appear.

This dialog box and its behavior are identical to the dialog box Modal Composition—Minerals FoM, so the reader is referred to section 6.2.2 for further information.

6.2.4 Size Distribution

Selection of a Size Distribution FoM computation causes the Size Distribution FoM dialog 

box to appear (fig. 32).

Pressing the Close button closes the dialog box and terminates FoM computation.

Pressing the Start Calculation button initiates computation of the Size Distribution FoM.
39

Figure 31. Modal Composition—General FoM dialog box.

Figure 32. Size Distribution FoM dialog box.

Fractions for size distribution are required to sum to unity. In practice however, fractions 

may not sum exactly to unity because of numerical round off. Therefore, a band around unity 

may be defined that is considered unity for summing purposes. Thus, sums that fall in the range 

1 ± Band are considered to be 1. The default value for Band is 0.001 so that all sums between 
40

0.999 and 1.001 are considered to be 1. The value of Band may be set to different values if the 

default is not appropriate.

The dialog box also allows the user to specify a Maximum RFD Difference. Recall that the 

Size Distribution FoM is computed by comparing two RFDs and that such FoMs are subject to 

a maximum error constraint. If the difference between the reference RFD and the simulant RFD 

exceeds the Maximum RFD Difference, then the FoM is set to zero. The default value for the Maximum RFD Difference is 0.2. This dialog box allows the user to specify a different value. The actual 

largest difference between the reference RFD and the simulant RFD is computed and displayed on 

a graph if the Plot option is checked.

Checking the box labeled Plot generates a series of plots of the reference RFD, the simulant 

RFD, and the difference of the reference and simulant RFDs. Additionally, the largest difference 

between the reference RFD and the simulant RFD is computed and displayed. These plots (fig. 33) 

are provided as visual aids to the FoM computation.

Figure 33. Size Distribution histogram plots.

6.2.5 Shape—Aspect Ratio

Selection of a Shape—Aspect Ratio FoM computation causes the Shape—Aspect Ratio 

FoM dialog box shown in figure 34 to appear. This FoM computation is an RFD computation just 
41

like the Size Distribution FoM computation; therefore, this dialog box is just like the Size Distribution Dialog box, with the exception that the computations can occur over multiple size ranges.

Pressing the Close button closes the dialog box and terminates FoM computation.

Pressing the Start Calculation button initiates computation of the Size Distribution FoM.

Figure 34. Shape—Aspect Ratio FoM dialog box.

Fractions for size distribution are required to sum to unity; in practice however, fractions 

may not sum exactly to unity because of numerical round off. Therefore, a band around unity 

may be defined that is considered unity for summing purposes. Thus, sums that fall in the range 

1 ± Band are considered to be 1. The default value for Band is 0.001 so that all sums between 0.999 

and 1.001 are considered to be 1. The value of Band may be set to different values if the default is 

not appropriate.

The dialog box also allows the user to specify a Maximum RFD Difference. Recall that the 

Shape—Aspect Ratio FoM is computed by comparing two RFDs and that such FoMs are subject 

to a maximum error constraint. If the difference between the reference RFD and the Simulant 

RFD exceeds the Maximum RFD Difference, then the FoM is set to zero. The default value for the 

Maximum RFD Difference is 0.2. This dialog box allows the user to specify a different value. The 

actual largest difference between the reference RFD and the simulant RFD is computed and displayed on a graph if the Plot option is checked.

Checking the box labeled Plot generates a series of plots of the reference RFD, the simulant 

RFD, and the difference of the reference and simulant RFDs. Additionally, the largest difference 
42

between the reference RFD and the simulant RFD is computed and displayed. The plots in figure 35 are provided as visual aids to the FoM computation and are similar to the ones shown for 

Size Distribution in figure 33.

Figure 35. Shape—Aspect Ratio FoM graphics output.

6.2.6 Shape—Angularity

Selection of a Shape—Angularity FoM computation causes the Shape—Angularity FoM 

dialog box shown in figure 36 to appear.

This dialog box and its behavior are identical to the dialog box Shape—Aspect Ratio FoM, 

so the reader is referred to section 6.2.5 for further information. Figure 37 presents examples of the 

Shape—Angularity FoM graphics output.
43

Figure 36. Shape—Angularity FoM dialog box.

Figure 37. Shape—Angularity FoM graphics output.
44

6.2.7 Density

Selection of a Density FoM computation causes the FoM Messages (see section 6.3) and 

Density FoM dialog box shown in figure 38 to appear.

Figure 38. Density FoM dialog box.

Pressing the Close button closes the dialog box and terminates FoM computation.

Pressing the Start Calculation button initiates computation of the Density FoM.

Checking the box labeled Plot will produce a set of bar graphs as shown in figures 39 and 

40. The reference density categories (mean specific gravity, minimum bulk density, and maximum 

bulk density) and the simulant density categories as separate plots are shown in figure 39. The reference and simulant density categories in a combined plot and the difference of the reference and 

simulant density categories are shown in figure 40. These plots are provided as visual aids to the 

FoM computation and are similar to the ones shown for modal composition in figures 26 and 27.
45

Figure 39. Density FoM graphics output, page 1.

Figure 40. Density FoM graphics output, page 2.
46

6.3 Figure of Merit Messages and Saving Results

When an FoM calculation is initiated, any messages resulting from the calculation and the 

results of the calculation are displayed in the scrolling FoM Messages window shown in figure 41.

This window captures errors, warnings, and informational messages. It also contains the 

results of the FoM calculation by default.

This window has two menus, Window and Options, that contain the menu items described 

in sections 6.3.1 and 6.3.2.

Figure 41. FoM Messages window.

6.3.1 Window Menu

Figure 42 is a depiction of the Window menu.

Figure 42. Window menu.

The Window menu contains the following menu items:

• Save Messages: Saves the contents of the window to a text file, so that a record of the FoM 

computations may be made.
47

• Clear Messages: Clears the contents of the window.

• Maximize Window: Maximizes the FoM Messages window. The window may also be resized by 

grabbing and dragging the top or bottom borders. Dragging on the title bar moves the window.

• Restore Window: Restores the FoM Messages window to its default size and location.

• Close: Closes the FoM Messages window. It may be reopened by selecting the 

Window>>Messages menu item.

6.3.2 Options Menu

Figure 43 is a depiction of the Options menu. 

Figure 43. Options menu.

The Options menu contains the following menu items:

• Include FoM: Includes the FoM computation result in the FoM Message window. This is 

checked by default.

• Include Input Data: Input data refers to the composition vectors, the size distribution vectors, 

the shape distribution data, and the density data as read from the reference and simulant work 

sheets. By checking ‘Include input data’ the raw inputs that were used for the FoM calculation 

can be captured in the FoM Messages window. These may then be saved for output if the user 

saves the contents of the FoM Messages window.

• Include Standardized Data: Raw input data is manipulated in various ways within the FoM software, such as converting to common units or adjusting composition vectors so that the reference 

and simulant vectors are commensurate. Input data that has been manipulated in some form or 

fashion is referred to as standardized data. By checking Include Standardized Data, these data 

are included in the FoM Messages window.

• Customize Font: Allows the user to choose the font and font size for text displayed in the FoM 

Messages window. Choosing a monospaced font (default) allows columns to line up. Font type 

and size selections are remembered between each execution of the FoM software.
48

6.4 Figure of Merit Menu Descriptions

6.4.1 File Menu

The FoM File menu is depicted in figure 44.

Figure 44. FoM File menu.

The File menu contains the following menu items:

• New...: Creates a new empty template file and prompts the user where to save this file. File may 

subsequently be opened by clicking on the label Reference or Simulant in the main window of 

the FoM software or externally with Excel.

• Open: This menu item contains the following submenus:

– Reference: If no reference file has been opened (the reference file field containing the path 

to reference file under the label Reference is blank), this opens the standard dialog box for 

retrieving files. Otherwise, if a reference file has been opened (field containing path to reference file under the label Reference contains a path), it opens the file in the reference file field 

under the label Reference.

– Simulant: If no simulant file has been opened (the simulant file field containing path to simulant file under the label Simulant is blank), this opens the standard dialog box for retrieving 

files. Otherwise, if a simulant file has been opened (field containing path to simulant file under 

the label Simulant contains a path), it opens the file in the simulant file field under the label 

Simulant.

• Close: This menu item contains the following submenus:

– Reference: Closes the reference file but leaves the name and path to the reference file in the 

reference file field.

– Simulant: Closes the simulant file but leaves the name and path to the simulant file 

in the simulant file field.

• Exit FoM: Terminates execution of the FoM software.

6.4.2 Window Menu

The FoM Window menu is depicted in figure 45.
49

Figure 45. FoM Window menu.

The FoM Window menu contains the following menu items:

• Hide All: Hides all open dialog windows.

• Reference: Maximizes the Excel Reference file window.

• Simulant: Maximizes the Excel Simulant file window.

• FoM: This menu item contains the following submenus:

– Modal Composition: This menu contains the following submenus.

 • Minerals: Opens the Modal Composition—Minerals dialog box, see section 6.2.2.

 • General: Opens the Modal Composition—General dialog box, see section 6.2.3.

– Size Distribution: Opens the Size Distribution dialog box, see section 6.2.4.

– Shape: This menu contains the following submenus.

 • Aspect Ratio: Opens the Shape—Aspect Ratio dialog box, see section 6.2.5.

 • Angularity: Opens the Shape—Angularity dialog box, see section 6.2.6.

– Density: Opens the Density dialog box, see section 6.2.7.

• Close All MATLAB Plots: Closes all open plot windows, also see section 6.5.

• Messages: Opens the FoM Messages dialog box, see section 6.3.

6.4.3 Help Menu

The FoM Help menu is depicted in figure 46.

Figure 46. FoM Help menu.
50

The FoM Help menu contains the following menu items:

• Contents: Opens the Help window from which further help for the FoM software may be 

obtained.

• About FoM: Opens the About dialog box.

6.5 Plot Windows Help

FoM plot windows contain three menus, File, Graph, and Gallery that may be used to 

fiddle with the plots. FoM plot windows also contain a toolbar known as the Plot Toolbar. In the 

parlance of the MathWorks, plot windows are known as figure windows and the Plot Toolbar is 

known as the Figure Toolbar. Further descriptions are found in sections 6.5.1 through 6.5.4.

6.5.1 File Menu

The FoM plot windows File menu is depicted in figure 47.

Figure 47. FoM plot windows File menu.

The FoM plot windows File menu contains the following menu items:

• New: Contains the submenu Figure, which opens a new plot window.

• Open...: Opens the standard dialog box for retrieving files.

• Close: Closes the current plot window.

• Save: Saves the current plot window. If window has not been saved before, opens the standard 

 dialog box for saving files.

• Save As...: Opens the standard dialog box for saving files.
51

• Export Setup...: Allows saving a plot in a format that can be used by another application such 

as the standard graphics file formats TIFF or EPS. For additional information see: 

<http://www.mathworks.com/help/techdoc/index.html>.

• Print Preview...: Opens a dialog box for previewing and selecting options for printing a plot 

window. For additional information see: <http://www.mathworks.com/help/techdoc/index.html>.

• Print...: Opens the standard dialog box for printing files to print the plot window.

6.5.2 Graph Menu

The FoM plot windows Graph menu (fig. 48) contains the menu items listed below. Certain 

menu items are graph specific, meaning that the function is performed on a selected graph. Graph 

selection occurs by clicking on the graph of interest. Selecting the menu item then performs the 

action.

Figure 48. FoM plot windows Graph menu.

• Labels...: For a selected graph, brings up a dialog box, shown in figure 49, where the user may 

specify a graph title, an X axis label, and a Y axis label (and Z axis label for three-dimensional 

(3-D)).
52

Figure 49. Labels dialog box.

If labels already exist, then the labels fields will be populated with the respective labels from 

the graph. Selecting another graph while the Labels dialog box is open causes the label fields to 

become repopulated with the labels from the new graph unless the Lock button is depressed. If the 

Lock button is depressed, then the labels are locked. In this case, pressing OK or Apply causes the 

locked labels to be applied to the new graph.

– OK: Applies the labels to the graph and closes the Labels dialog box.

– Apply: Applies the labels to the graph but leaves the Labels dialog box open.

– Lock: Locks the text in the labels fields if depressed. If not depressed, then fields repopulate 

when a new graph is selected.

– Cancel: Closes the Labels dialog box without changing any labels.

• Grid: For a selected graph, toggles grid lines on the graph.

• Print: Opens the standard dialog box for printing files to print the plot window.

• Axis Equal: For a selected graph, causes the axis scale factors (data length/physical length) 

to be the same in X and Y (and Z for 3-D plots) so that circles (spheres) plot like circles instead 

of ellipses (ellipsoids). Changes the axes data length but keeps the physical length the same.

• Axis Vis3D: For a selected graph, causes the axis scale factors (data length/physical length) 

to be the same in X and Y (and Z for 3-D plots) so that circles (spheres) plot like circles instead 

of ellipses (ellipsoids). Changes the axes physical length but keeps the data length the same.

• Axis Normal: For a selected graph, restores the axes to their original scaling if changed by Axis 

Equal or Axis Vis3D.

• Axis Off: Toggles the visibility of the axes and grid if one exists. Note that making the axes invisible also makes any labels invisible including the graph title, X-axis label, and Y-axis label.
53

• Axis Scaling: For a selected graph, brings up the Axis Scaling dialog box, shown in figure 50, where 

the user may manually specify axes data limits. For the X and Y axes (and Z axes if a 3-D plot), the 

minimum and maximum axes limits may be specified. When the dialog box opens, the axes limit 

data fields are populated with the current graph axes limits. The current graph may be designated 

by clicking in it. Selecting another graph with the Axis Scaling dialog box open causes the axes 

limit data fields to become repopulated with the limits from the new graph unless the Lock button 

is depressed. If the Lock button is depressed, the axes limit data is locked. In this case, pressing 

OK or Apply causes the locked data values to be applied as axes limits to the new graph.

Figure 50. Axis Scaling dialog box.

 – OK: Applies the axes data values to the graph and closes the Axis Scaling dialog box.

 – Apply: Applies the axes data values to the graph but leaves the Axis Scaling dialog box open.

 – Lock: Locks the axes data values in the axes limit data fields if depressed. If not depressed, 

 then fields repopulate when a new graph is selected.

– Cancel: Closes the Axis Scaling dialog box without changing any axes limits.

– Auto-Scale: Causes the axes to be automatically scaled.

 – Zoom: See Zoom below.

• Auto-Scale: For a selected graph, causes the axes to be automatically scaled.

• Zoom: Changes the cursor to a cross-hairs cursor and allows zooming in on a portion of the 

graph. Dragging the cross-hairs cursor creates a zoom box to which the axes will rescale. Right 

clicking causes rescaling to the previous zoom box. Pressing the Enter key on the keyboard terminates zooming and leaves the graph at the last zoom box scaling.

Note that while the cross-hairs cursor is displayed, different graphs may be zoomed by dragging within them. The zooming function remembers the level of zooming for each graph, so they 

may be individually unzoomed. However, once zooming is terminated with the Enter key, unzooming information is lost.

• Help: Displays the help text.
54

6.5.3 Gallery Menu

The FoM plot windows Gallery menu (fig. 51) contains the menu items listed below. These 

menu items are graph specific, meaning that the function is performed on a selected graph. Graph 

selection occurs by clicking on the graph of interest. Selecting the menu item then performs the 

action.

Figure 51. Gallery menu.

• Linear Plot: For the selected graph, changes the axes scaling to linear scaling.

• Log-Log: For the selected graph, changes the X- and Y-axes scaling to logarithmic.

• Semi-Log X: For the selected graph, changes the X-axis scaling to logarithmic.

• Semi-Log Y: For the selected graph, changes the Y-axis scaling to logarithmic.

• Help: Displays this help text.

6.5.4 Plot Toolbar

The Plot toolbar shown in figure 52 is provided by The MathWorks, Inc. In MathWorks 

parlance, this is also known as the Figure toolbar. Certain tools are graph specific, meaning that 

they work on a selected graph. Graph selection occurs by clicking on the graph of interest either 

with the tool or with the mouse pointer.

Figure 52. Plot toolbar.

Further help on the use of the Plot toolbar may be found at: <http://www.mathworks.com/

help/techdoc/index.html>.
55

The icons from left to right in figure 52 have the following names and functions listed 

in table 1:

Table 1. Plot toolbar icon names and functions.

New Plot: Creates a new plot window.

Open File: Displays the open file dialog box for opening a file.

Save Plot: Displays the save file dialog box for saving the FoM graphs.

Print Plot: Displays the print dialog box for printing the FoM graphs.

Zoom In: Allows zooming in on a portion of the graph by clicking or dragging to create a zoom box (scale of axes is changed). Right 

clicking with this tool displays a drop-down menu from which further options may be selected, including Reset to Original View.

Zoom Out: Allows zooming out by clicking on a graph (scale of axes is changed). Right clicking with this tool displays a drop-down 

menu from which further options may be selected, including Reset to Original View.

Pan: Allows a graph to be panned (axes limits are changed but scale is not). Right clicking with this tool displays a drop-down 

menu from which further options may be selected, including Reset to Original View.

Rotate 3D: Allows 3-D rotation of the plot axes and associated plot. This works for two-dimensional plots also. Right clicking with 

this tool displays a drop-down menu from which further options may be selected, including Reset to Original View.

Data Cursor: Allows pickoff of data values on a graph. Clicking on a portion of a curve displays the abscissa (X) and ordinate (Y) 

values. Right clicking with this tool displays a drop-down menu from which further options may be selected.

Insert Colorbar: Inserts a color bar for a selected graph. A color bar is a legend with values for graphs containing items whose 

colors indicate values.

Insert Legend: Inserts a legend for a selected graph. The legend text may then be edited by double clicking on the default text.

6.6 Limitations of Using Excel With the Figure of Merit Software

The FoM software accesses the Excel data files via ActiveX Automation. Limitations of this 

interface require that only one instance of Excel is running while the FoM software is running. The 

FoM software must launch this instance of Excel.

If an instance of Excel.exe is running when the FoM software is started, the error message 

of figure 53 will display and the user will be prompted to terminate the Excel.exe process before 

running the FoM software.

If the Excel process was initiated from Windows, it should be terminated by using the 

File>>Exit option from within Excel.

If the FoM software terminates abnormally, it is possible that an Excel.exe process will be 

left running. If this is the case, the only way to terminate this process is to use the Windows Task 

Manager to end the Excel.exe process tree. This termination may possibly cause loss of any unsaved 

changes in the Excel data files.
56

Figure 53. Excel is already running error message.

6.7 Copyrights

The following copyrights are germane to this Technical Memorandum (TM):

• Microsoft® is a registered trademark of Microsoft Corporation.

• LabWindowsTM/CVITM © 2008 by National Instruments. All rights reserved.

• MATLAB, © 1984–2008 by The MathWorks.

• FoM Software and FoM Software © 2007, 2008 by Teledyne Brown Engineering (TBE), Inc. All 

rights reserved.
57

7. INSTALLATION NOTES

FoM Software is a Microsoft Windows-based application developed and maintained 

by TBE, Huntsville, Alabama for Marshall Space Flight Center (MSFC).

7.1 Minimum System Requirements

Minimum system requirements have not been established at this time; however, the FoM 

software has been tested with the following system configurations:

• Microsoft Windows 2000® and Windows XP®.

• 512 MB RAM.

• Microsoft Excel 2000® and Microsoft Excel 2003®.

• Mass storage requirements are minimal (<0.5 GB).

7.2 Required Components for Execution of Figure of Merit Software

The following components are required for the execution of FoM software:

• FoM software is a National Instruments LabWindowsTM/CVITM 8.5-based custom graphical 

user interface with MATLAB-based custom FoM functions used to compute FoMs.

• National Instruments LabWindowsTM/CVITM 8.5 Run-Time Environment (RTE) is automatically installed in the application directory with the FoM software during installation. This RTE 

will automatically be uninstalled when the FoM software is uninstalled.

MATLAB Compiler Runtime (MCR) 7.9 is licensed and installed separately. TBE distributes the MCR at no cost to the FoM software user. This is a one-time installation and does not 

need to be repeated for new releases of the FoM software.

• Excel 2000 (or later) is used to generate input data for the FoM software and must be installed 

 on the system with the FoM software. It is the responsibility of the system owner to purchase and 

 install the Excel software.
58

7.3 Installation Instructions

The FoM software package consists of two separate software components that require two 

installations:

(1) The FoM software proper, herein denoted as FoM software.

(2) An engine from The MathWorks, Inc. known as the MATLAB MCR that powers 

the numerical routines in the FoM software.

Additionally, the FoM software uses the Excel software, which the user must acquire 

and install separately. The National Instruments LabWindowsTM/CVITM RTE is automatically 

installed when the FoM software is installed.

Once the MCR has been installed, it will not be necessary to install it again for future FoM 

software releases, except if the future software release requires a newer version of the MCR.

7.4 Installation of MATLAB Compiler Runtime

This installation step may be skipped if the user has previously installed the MCR version 

7.9 on the PC that the FoM software is being installed, or if MATLAB, version 7.7 (release 2008b) 

is already installed on the PC that the FoM software is being installed. The version of MATLAB 

installed on a PC may be ascertained by launching MATLAB, then entering the command ‘>> ver’ 

at the command line. The Command Window shown in figure 54 will appear.

Figure 54. MATLAB responds with version information.
59

7.5 Specific Steps

Step 1: The user must have administrative privileges to install the MCR on a target machine since it 

modifies both the system registry and the system path. Running the MCRInstaller after the 

MCR has been set up on the target machine requires only user-level privileges.

Step 2. In the FoM Installation folder, open the folder titled MCRInstaller. In this folder, open the 

folder titled MCR installer XXXXx (XXXXx is the release version of the installer). Launch 

the application MCRInstaller shown in figure 55.

Figure 55. MCRInstaller.

Step 3. The initial prompt will be Choose Setup Language. Select English or Japanese and click on 

OK to continue. The Choose Setup Language dialog box in figure 56 will appear.

Figure 56. Choose Setup Language.

Step 4. If the Microsoft Visual C++ Redistributable Package is already installed on the machine 

that the MCR is being installed, then the dialog box in figure 57 will not appear and the 

user may proceed to the next step. Otherwise, click on Install to continue.

Figure 57. InstallShield Wizard MATLAB(R).
60

Step 5: This will bring up the dialog boxes shown in figures 58 and 59 in sequence, as the installation gets under way. No action is required by the user until step 6 unless the user wishes to 

cancel the installation.

Figure 58. InstallShield Wizard (prepare to install).

Figure 59. Windows Installer.

Step 6: The InstallShield Wizard will now unpack the MCRInstaller, which will bring up the 

InstallShield Wizard for MATLAB Compiler Runtime box shown in figure 60. Select 

Next > to continue.
61

Figure 60. MATLAB(R) Compiler Runtime 7.9.

Step 7: Enter the User Name and Organization when reaching the Customer Information prompt 

(fig. 61). Then press Next >.

Figure 61. MATLAB(R) Customer Information.

Step 8: This will bring up the Destination Folder (fig. 62) prompt for installation of the MCR. The 

default destination is ...\Program Files\MATLAB\MATLAB Compiler Runtime\. Change 

the destination if the default is unacceptable, then press Next >.
62

Figure 62. MATLAB(R) Destination Folder.

Step 9: This brings up the Ready to Install the Program (fig. 63) prompt. Press Install to begin the 

installation.

Figure 63. MATLAB(R) Ready to Install the Program.
63

Step 10. Installation begins (fig. 64).

The user may be notified that .NET Framework is not installed (fig. 65). If this prompt is 

received, press OK to continue. The FoM software does not currently require .NET Framework.

Figure 64. Installing MATLAB(R) Computer Runtime 7.9.

Figure 65. Installing MATLAB(R) Computer Runtime (.NET Framework not installed).
64

Step 11. Upon notification that the installation has completed, press Finish to finish (fig. 66).

Figure 66. MATLAB(R) Installation Wizard Completed.

7.6 Installation of Figure of Merit Software

If the user has previously installed the FoM software, the old version of the software should 

be uninstalled before a new version is installed. To uninstall a previous version of the FoM software, go to the Start button, then Settings, then Control Panel and open the Add or Remove Programs control panel. Scroll through the list of currently installed programs until Figures of Merit 

is found. Select Figures of Merit and press Remove to uninstall the program. If Figures of Merit is 

not found in the list of currently installed programs, then it is not installed and no further uninstallation is necessary.

7.7 Specific Steps

Step 12: The user must have administrative privileges to install the FoM software on a target 

machine since it modifies both the system registry and the system path. Running the FoM 

software after it has been set up on the target machine requires only user-level privileges.

Step 13: In the FoM Installation folder, open the folder titled FoM Installer (fig. 67). Launch the 

application setup.

Figure 67. FoM setup Installer.
65

Step 14: The installer responds with the initialization screen shown in figure 68 after launching.

Figure 68. Figures of Merit.

Step 15: The initial prompt will be Destination Directory (fig. 69). Change the destination if the 

default is unacceptable, then press Next >>.

Figure 69. Destination Directory.

Step 16: This brings up the License Agreement (fig. 70). Note the restriction on redistribution of 

the MCR. The user may not further distribute the MCR. Each copy of the MCR must be 

requested from one of the points of contact in the section Contact Information. In order 

to install the FoM software, the user must agree to the terms of the License. Press Next >> 

to continue.
66

Figure 70. License Agreement.

Step 17: This brings up the Start Installation prompt (fig. 71). Select Next >> to begin installation.

Figure 71. Start Installation.

Step 18: Installation begins as indicated by the screen shown in figure 72.

Step 19: Upon notification that the installation has completed, press Finish to finish (fig. 73).
67

Figure 72. Overall Progress.

Figure 73. Installation Complete.

7.8 Messages/Errors

During installation of the MATLAB MCR, the user may receive the following error 

messages. Please respond accordingly.
68

If the message in figure 74 is received:

Figure 74. .NET Framework is not installed.

Recommended response:

• Select OK to continue. The FoM software does not currently require .NET Framework.

When attempting to execute the FoM software, you may receive these system messages. 

Please respond accordingly.

A popup dialog containing the message shown in figure 75 (or similar) appears when 

attempting to execute the FoM software. This message occurs if the MCR is not installed.

Figure 75. Unable to Locate Component.

Recommended response:

• Press the OK button, then install the MathWorks MCR by running the MCRInstaller.exe 

application. See section 7.4.

Popup dialogs containing the messages shown in figures 76 and 77 (or similar) appear when 

attempting to open a reference or simulant Excel file. These messages occur if Excel is not installed.
69

Figure 76. Microsoft Excel Automation.

Figure 77. Excel Launch Error.

Recommended response:

• Press the OK button then install Microsoft Excel. 

Complete uninstallation of the FoM software package will require uninstallation of the 

MCR and the FoM software.

7.9 Uninstallation of the Figure of Merit Software

To uninstall the FoM software, go to the Start button, then Settings, then Control Panel 

and open the Add or Remove Programs control panel. Scroll through the list of currently installed 

programs until Figures of Merit is found. Select Figures of Merit and press Remove to uninstall 

the program. If Figures of Merit is not found in the list of currently installed programs, then it is 

not installed and no further uninstallation is necessary.

7.10 Uninstallation of the MathWorks MATLAB Compiler Routine

To uninstall the MCR, go to the Start button, then Settings, then Control Panel and open 

the Add or Remove Programs control panel. Scroll through the list of currently installed programs 

until MATLAB Compiler Runtime X.X is found (where X.X is the version number). Select MATLAB Compiler Runtime X.X and press Remove to uninstall the program. If MATLAB Compiler 

Runtime X.X is not found in the list of currently installed programs, then it is not installed and no 

further uninstallation is necessary.
70

8. TROUBLESHOOTING

8.1 Installation Troubleshooting

During installation of the MCR or FoM software or when the FoM software is executed, 

the user may receive the following system messages. Please respond accordingly.

(1) The following message is received: .NET Framework is not installed. If the user requires it, 

select Cancel and install .NET Framework first. Otherwise, select OK to continue.

(a) Recommended response: Select OK to continue. The FoM software does not currently 

require .NET Framework.

8.2 Execution Troubleshooting

When attempting to execute the FoM software, the user may receive the following system 

messages. Please respond accordingly.

(1) The popup dialog of figure 78 (or similar) appears when attempting to execute the FoM 

software. This message occurs if the MathWorks MCR is not installed.

(a) Recommended response: Press the OK button, then install the MathWorks MCR by 

running the MCRInstaller.exe application.

Figure 78. Unable to locate FoM DLL error message.

(2) The popup dialog of figure 41 appears when attempting to execute the FoM software. This 

message occurs if Excel is running when the FoM software starts.

(a) Recommended response:

 i. Press the OK button.

ii. If Excel is running, exit Excel.

 iii. Otherwise, launch Windows Task Manager by right clicking on the task bar at the 

 bottom of the window and selecting Task Manager from the popup menu.

 iv. In Task Manager, go to the Processes tab, find the running Excel process 

 (EXCEL.EXE), select it, and press the End Process Tree button to terminate 

 the process.
71

(3) The popup dialog of figure 79 may appear when attempting to select a reference (or simulant) 

data file. This message occurs if the pathname of the data file exceeds the Windows limitation 

of 256 characters. Note: The Simulant Data.xls in this example popup is the selected filename 

without the full pathname.

(a) Recommended response:

 i. Press the OK button.

ii. Move the data file to a folder at a higher level to shorten the full pathname, or shorten 

the folder name(s) in the path of this file.

Figure 79. Path depth error message.
72

9. VERSION DESCRIPTION DOCUMENT

FoM software is a Microsoft Windows-based application developed and maintained by 

TBE, Huntsville, AL for the MSFC. This TM records the versions of the components that form a 

complete package for release. It also describes the versions of software that were used to create the 

FoM software.

9.1 Figure of Merit Software Version

This TM describes component versions for version 2.0 of the FoM software.

9.2 Figure of Merit Software Package Components

The FoM software package is comprised of a primary application and two dynamic link 

libraries (DLLs) developed by TBE under two separate development systems: MATLAB by The 

MathWorks and LabWindows/CVI by National Instruments.

9.2.1 MATLAB Figure of Merit Dynamic Link Library (fom_lib.dll) Software Components

The MATLAB software (fom_lib.dll) component version numbers are listed in table 2.

Table 2. DLL package.

Software File Type Version Date

fom_lib_release_26.zip DLL Archive 26 December 15, 2008

9.2.1.1 MATLAB Figure of Merit Dynamic Link Library Code. The MATLAB FoM DLL 

source code files are not assigned individual version numbers except for the two primary components. The files that comprise Version 26 of the MATLAB FoM DLL are dated and time-stamped 

(Central Time Zone) as shown in tables 3 and 4.

Table 3. Matlab FoM DLL primary components.

Software Files Type Version Date

fom_bar.m

fom_rfd.m

m Function

m Function

Rev 4

Rev 4

December 15, 2008

December 15, 2008
73

Table 4. Matlab FoM DLL support components.

Software Files Type Date Time

isnumericscalar.m

isnumericvector.m

multigraph.m

multigraph_init_fom.m

plot_menus_fom

textf.m

time_stamp.m

xticklabel_rotate.m

Gallery Menu fom.mht

Graph Menu fom.mht

m Function

m Function

m Function

m Function

m Function

m Function

m Function

m Function

HTML Help

HTML Help

September 09, 2008

September 09, 2008

August 29, 2007

October 29, 2007

June 02, 2008

August 29, 2006

February 27, 2004

November 07, 2008

March 21, 2008

March 21, 2008

2:45 pm

2:46 pm

2:31 pm

9:15 am

3:16 pm

11:44 am

5:05 pm

10:35 am

1:08 pm

1:10 pm

9.2.2 LabWindows/C for Virtual Instrumentation Figure of Merit Software Components

The LabWindows/CVI software component version numbers are shown in tables 5 and 6.

Table 5. LabWindows/CVI primary components.

Software Files Type Version Date

FoM Application (FoM.exe)

FoM_MATLAB (FoM_MATLAB.dll)

Application

Application Extension

2.0 (TBE)

2.6 (TBE)

December 22, 2008

December 22, 2008

Table 6. LabWindows/CVI support components.

Software Files Type Version Date

excel2000.fp

animate.fp

toolbox.fp

Psapi.lib

version.lib

fom_lib.dll (from Matlab Software in section 2.1)

FoM Help File.chm

Instrument

Instrument

Instrument

Library

Library

Application Extension

Compiled HTML Help File

CVI 8.5

CVI 8.5

CVI 8.5

CVI 8.5

CVI 8.5

26 (TBE)

From Rev 1 of FoM UG

October 23, 2007

October 23, 2007

October 23, 2007

October 23, 2007

October 23, 2007

December 15, 2008

December 22, 2008

9.2.2.1 Figure of Merit Application (FoM.exe) Code. The FoM Application (FoM.exe) 

source, include, and user interface files are not assigned individual version numbers. The files that 

comprise Version 2.0 of the FoM Application code are dated and time stamped (Central Time 

Zone) as shown in table 7.

9.2.2.2 Figure of Merit MATLAB Dynamic Link Library (FoM_Matlab.dll) Code. The 

FoM MATLAB DLL (FoM_Matlab.dll) Version 2.6 is the application extension used with the 

FoM Application Version 2.0. FoM_Matlab.dll Version 2.6 code is comprised of files dated and 

time stamped as shown in table 8.
74

Table 7. Files that comprise Version 2.0 of the FoM application code.

Source Files Date Time

FoM_Main.c

FoM_Menu.c

FoM_Composition.c

FoM_SizeDist.c

FoM_Shape.c

FoM_Density.c

FoM_ExcelFunctions.c

FoM_SharedFunctions.c

December 19, 2008

December 10, 2008

December 09, 2008

November 10, 2008

December 09, 2008

November 10, 2008

October 14, 2008

December 09, 2008

4:50 pm

3:13 pm

3:45 pm

10:09 am

3:45 pm

10:09 am

12:55 pm

3:13 pm

Include Files Date Time

FoM_Globals.h

FoM_Displays.h

FoM_ExcelFunctions.h

FoM_MATLAB.h

December 09, 2008

December 08, 2008

October 14, 2008

October 21, 2008

3:21 pm

2:53 pm

12:55 pm

8:46 am

User Interface Files Date Time

FoM_Displays.uir December 10, 2008 2:59 pm

Table 8. FoM Matlab DLL (FoM_Matlab.dll) Version 2.6.

Source Files Date Time

fom_lib.c (glue code for fom_lib.dll)

mclmcrrt.c (glue code for mclmcrrt79.dll)

FoM_Matlab.c 

December 18, 2008

December 18, 2008

December 18, 2008

1:35 pm

3:38 pm

3:42 pm

Include Files Date Time

fom_lib.h

mclmcrrt.h

FoM_MatlabDisplays.h

FoM_Matlab.h

December 18, 2008

December 08, 2008

November 09, 2008

October 21, 2008

1:34 pm

1:26 pm

11:51 pm

8:46 am

User Interface Files Date Time

FoM_MatlabDisplays.uir November 09, 2008 11:52 pm

9.2.3 Excel Workbook

The Excel workbook version number is shown in table 9.

Table 9. Excel workbook version number.

Workbook File Version Date

FoM Template_1.2.1.xls 1.2.1 b December 12, 2008
75

9.2.4 Documentation

Document version numbers are shown in table 10.

Table 10. Document version numbers.

Document Files Version Date

Figures-of-Merit Algorithm Description

Figures-of-Merit Software User’s Guide

Figures-of-Merit Software Installation Notes

Figures-of-Merit Software License Agreement

Figures-of-Merit Software Release Notes

Figures-of-Merit Software Version Description Document

Rev 1

Rev 1

Rev 1

2

–

–

December 31, 2008

December 31, 2008

December 31, 2008

–

December 31, 2008

December 31, 2008

9.3 Ancillary Software (Development Environment)

This section lists the versions of software tools used to develop the FoM software.

9.3.1 MATLAB Software

The software file number for Compile Script is listed in table 11.

Table 11. Compile script.

Software File Version Date

mcc_lib_script.m – December 05, 2008

The MathWorks software is identified in table 12.

Table 12. MathWorks software.

Software Version Date

Matlab Compiler

Lcc-win32 C (C compiler)

Matlab Compiler Runtime (MCR)

4.9

2.4.1

7.9

–

–

–

9.3.2 LabWindows/ C for Virtual Instrumentation Software

Workspace and Project Files software files are listed in table 13.
76

Table 13. Workspace and project files.

Software File Type Date

FoM.cws (includes both .prj files)

FoM.prj (Build for FoM.exe)

FoM_Matlab.prj (Build for FoM_Matlab.dll)

Workspace

Project

Project

December 29, 2008

December 22, 2008

December 22, 2008

National Instruments software is listed in table 14

Table 14. National Instruments software.

Software Version Date

LabWindows/CVI Development System

LabWindows/CVI Runtime Environment

8.5

8.5

–

–
77

10. SUPPORT

10.1 About Figures of Merit Software

FoM software is a Microsoft Windows-based application developed and maintained 

by TBE, Huntsville, AL for MSFC.

The FoM software is comprised of and/or uses the following custom and commercially 

available software components that must be installed on the target system:

• FoM software is a National Instruments LabWindowsTM/CVITM 8.5-based custom graphical 

user interface and MATLAB-based custom FoM functions used to generate FoM.

– LabWindows/CVI, © 2008 by National Instruments. All rights reserved.

• National Instruments LabWindows/CVI 8.5 RTE is automatically installed in the application 

directory with the FoM software during this installation. This RTE will automatically be uninstalled when the FoM software is uninstalled.

• MathWorks MCR is licensed and installed separately. The MCR is distributed by TBE at no cost 

to the FoM software user. This is a one-time installation and does not need to be repeated for 

new releases of the FoM software.

– MATLAB, © 1984–2008 by The MathWorks, Inc.

• Microsoft Excel 2000 (or later) is used to generate input data for the FoM software and must 

be installed on the system with the FoM software. It is the responsibility of the system owner 

to purchase and install the Microsoft Excel software.

– Microsoft is a registered trademark of Microsoft Corporation.
78

11. CONTACT INFORMATION

For technical support, contact:

Douglas L. Rickman

Global Hydrology and Climate Center

NSSTC/MSFC/NASA

ph. 256–961–7889 (fax –7389, alt. fax –7788)

Douglas.L.Rickman@nasa.gov

For algorithm and software support, contact:

Hans D. Hoelzer

Teledyne Brown Engineering

ph. 256–726–1632

hans.holzer@tbe.com
79

12. LICENCES FOR THE FIGURES OF MERIT SOFTWARE

Version 2.0

© 2007, 2008 by Teledyne Brown Engineering, Inc.

Developed by TBD, Inc. for MSFC

All Rights Reserved.

12.1 License Agreement

The user should carefully read the following terms and conditions before using this software. Use of this software indicates the user’s acceptance of this license agreement and warranty.

12.2 Freeware

The user may use this product free of charge as an approved customer, vendor, and/or 

otherwise associated entity with NASA. FURTHER DISTRIBUTION OF THIS PRODUCT 

IS RESTRICTED BY THE TERMS DEFINED IN ‘USE AND RESTRICTIONS’ HEREIN.

12.3 Components

The FoM software package consists of two separate software components that are subject 

to different restrictions. These components are the FoM software proper (developed by TBE, Inc. 

and herein denoted as FoM software) and the MCR (a computational engine from The MathWorks, Inc.).

12.4 Disclaimer of Warranty

THE FIGURES OF MERIT SOFTWARE PACKAGE IS DISTRIBUTED ‘AS IS’ AND 

WITHOUT WARRANTIES AS TO PERFORMANCE OR MERCHANTABILITY OR ANY 

OTHER WARRANTIES WHETHER EXPRESSED OR IMPLIED. BECAUSE OF THE VARIOUS HARDWARE AND SOFTWARE ENVIRONMENTS INTO WHICH THIS PROGRAM 

MAY BE INSTALLED, NO WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE 

IS OFFERED. GOOD DATA PROCESSING PROCEDURE DICTATES THAT ANY PROGRAM BE THOROUGHLY TESTED WITH NON-CRITICAL DATA BEFORE RELYING 

ON IT. THE USER MUST ASSUME THE ENTIRE RISK OF USING THE PROGRAM.

FURTHERMORE, THIS LICENSE EXPLICITLY ALSO EXCLUDES THE MATHWORKS, INC. AND ITS LICENSORS FROM ALL LIABILITY FOR DAMAGES OR ANY 

OBLIGATION TO PROVIDE REMEDIAL ACTIONS. THE MATHWORKS HAS NO SUPPORT OR WARRANTY OBLIGATIONS, AND DISCLAIMS ALL LIABILITY, FOR THE 

FOM SOFTWARE APPLICATION DEVELOPED AND DISTRIBUTED BY TELEDYNE 

BROWN ENGINEERING, INC. FOR MARSHALL SPACE FLIGHT CENTER.
80

12.5 Use and Restrictions

(1) USE RESTRICTIONS. The FoM software was developed at the United States (U.S.) Government expense; thus, any U.S. Government agency has unlimited rights with regard to it. The restrictions in this paragraph apply to non-U.S. Government persons and entities. The FoM software is 

licensed not sold. TBE, Inc. owns the title, copyright, and the trade secret and other intellectual 

property rights in the FoM software and the copyright in the documentation, and reserves all rights 

not expressly granted to you in this Agreement. You agree that you will not rent, loan, lease, or 

sublicense the FoM software package, or use components of the FoM software package separately. 

You also agree not to attempt to reverse engineer, decompile, modify, translate, disassemble, discover the source code of, or create derivative works from any part of the FoM software package. 

You also agree not to authorize others to undertake any of these prohibited acts.

(2) EXPORT CONTROL. The FoM software is subject to export controls under the U.S. Export 

Administration Regulations. The FoM software may not be exported or reexported to entities 

within, or residents or citizens of, embargoed countries or countries subject to applicable trade 

sanctions, nor to prohibited or denied persons or entities without proper government licenses. 

Information about such restrictions can be found at the following Web sites: <http://www.treas.

gov/offices/enforcement/ofac/> and <www.bis.doc.gov/complianceandenforcement/ListsToCheck.

htm>. You are responsible for any violation of the U.S. export control laws related to the FoM 

software. By accepting this Agreement, you confirm that you are not a resident or citizen of any 

country currently embargoed by the U.S. and that you are not otherwise prohibited from receiving 

the FoM software.

(3) FURTHER DISTRIBUTION.

(a) You are hereby granted permission to duplicate and distribute the FoM software package 

and give exact copies of the original version to anyone within your organization working 

with you and for the same purpose for which you downloaded the FoM software package. 

Recipients of such copies must agree to the same licensing terms that you are agreeing to. 

You may distribute the FoM software package and documentation in its unmodified form 

via electronic means; however, you may not distribute the FoM software package on a 

server open to the public Internet. There is no charge for any of the above.

(b) You are specifically prohibited from charging or requesting donations for any such copies 

of the FoM software package, however made. You are also prohibited from distributing 

the FoM software package and/or documentation with other products (commercial or 

otherwise) without prior written permission.

(c) TBE, Inc. has limited rights to the deployment of the MATLAB Component Runtime 

libraries that are governed by a certain license agreement between TBE, Inc. and The 

MathWorks. This limitation allows for deployment of the MCR libraries only to specified customers. Thus, you are not allowed to distribute the MCR libraries or to place them 

on a public Internet Web site for download. Parties needing to obtain copies of the MCR 

libraries should contact TBE, Inc.
81

(4) SEPARATION OF COMPONENTS: The FoM software package product is licensed as a 

single product. Its component parts may not be separated for any use. Each component may have 

its own license agreement (Component Agreement). In the event of inconsistencies between this 

agreement and any Component Agreement, the terms of the Component Agreement shall control.

(5) APPLICABLE LAW:

(a) U.S.: If you acquired the software in the U.S., Alabama state law governs the interpretation 

of this agreement and applies to claims for breach of it, regardless of conflict of laws principles. The laws of the state where you live govern all other claims, including claims under 

state consumer protection laws, unfair competition laws, and in tort.

(b) Outside the U.S.: If you acquired the software in any other country, the laws of that country apply.

Microsoft is a registered trademark of Microsoft Corporation.

LabWindows/CVI, © 2008 by National Instruments. All rights reserved.

MATLAB, © 1984–2008 by The MathWorks, Inc.

Teledyne Brown Engineering, Inc.

P. O. Box 070007

Huntsville, AL 35807-7007

Attn: H. D. Hoelzer

hans.hoelzer@tbe.com
82
83

REFERENCES

1. Rickman, D.L.; Hoelzer, H.; Fourroux, K.; et al.: “Quantitative Technique for Comparing 

Simulant Materials Through Figures of Merit,” In Planetary and Terrestrial Mining Sciences 

Symposium (4th), June 10–13, NORCAT, Sudbury, Ontario, Canada, 2007.

2. Rickman, D.L.; Hoelzer, H.; Carpenter, P.; et al.: “A Quantitative Method for Evaluating Regolith Simulants,” Space Technology and Applications International Forum (STAIF 2007), pp. 957–

963, Albuquerque, NM: AIP Conference Proceedings, Vol. 880. doi:10.1063/1.2437539, 2007.

3. Schrader, C.M.; Rickman, D.L.; Stoeser, D.B.; and Hoelzer, H.: “Constraining Particle Variation in Lunar Regolith for Simulant Design,” In SPACE 2008, September 9–11, San Diego, CA: 

AIAA, 2008.

4. Slane, F.A.; and Rickman, D.L.: “Space systems–Lunar Simulants,” ISO TC 20/SC 14/

WG 4 ISO/CD 10788(E), Draft No. 6. spacewx.com. http://www.spacewx.com/Docs/ISO_

CD_10788_E.pdf>, accessed 2009.
84

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining 

the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing 

this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operation and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 

OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

 REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITOR’S ACRONYM(S)

11. SPONSORING/MONITORING REPORT NUMBER

12. DISTRIBUTION/AVAILABILITY STATEMENT

13. SUPPLEMENTARY NOTES

14. ABSTRACT

15. SUBJECT TERMS

16. SECURITY CLASSIFICATION OF:

a. REPORT b. ABSTRACT c. THIS PAGE

17. LIMITATION OF ABSTRACT 18. NUMBER OF

 PAGES

19a. NAME OF RESPONSIBLE PERSON

19b. TELEPHONE NUMBER (Include area code)

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18

Figures of Merit Software: Description, User’s Guide,

Installation Notes, Versions Descriptions, 

and License Agreement

H.D. Hoelzer,* K.A. Fourroux,* D.L. Rickman, 

and C.M. Schrader** 

George C. Marshall Space Flight Center

Marshall Space Flight Center, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 91

Availability: NASA CASI (443–757–5802)

Prepared by the Earth Sciences Office

* Teledyne Brown Engineering, Inc., Huntsville, Alabama, ** BAE Systems, Huntsville, Alabama

M–1313

Technical Memorandum

NASA/TM—2011–216464

lunar simulant, Figure of Merit, software, mathematics, use, license, quantative comparison, comparison 

of mixtures, comparison of particulates

01–03–2011

UU 94

NASA

U U U

Figures of Merit (FoMs) and the FoM software provide a method for quantitatively evaluating the quality of a regolith simulant 

by comparing the simulant to a reference material. FoMs may be used for comparing a simulant to actual regolith material, 

specification by stating the value a simulant’s FoMs must attain to be suitable for a given application and comparing simulants 

from different vendors or production runs. FoMs may even be used to compare different simulants to each other. A single FoM 

is conceptually an algorithm that computes a single number for quantifying the similarity or difference of a single characteristic 

of a simulant material and a reference material and provides a clear measure of how well a simulant and reference material match 

or compare. FoMs have been constructed to lie between zero and 1, with zero indicating a poor or no match and 1 indicating a 

perfect match. FoMs are defined for modal composition, particle size distribution, particle shape distribution, (aspect ratio and 

angularity), and density. This TM covers the mathematics, use, installation, and licensing for the existing FoM code in detail.

STI Help Desk at email: help@sti.nasa.gov

STI Help Desk at: 443–757–5802
The NASA STI Program...in Profile

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientific and Technical Information (STI) 

Program Office plays a key part in helping NASA 

maintain this important role.

The NASA STI Program Office is operated by 

Langley Research Center, the lead center for 

NASA’s scientific and technical information. The 

NASA STI Program Office provides access to 

the NASA STI Database, the largest collection of 

aeronautical and space science STI in the world. 

The Program Office is also NASA’s institutional 

mechanism for disseminating the results of its 

research and development activities. These results 

are published by NASA in the NASA STI Report 

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major significant 

phase of research that present the results of 

NASA programs and include extensive data 

or theoretical analysis. Includes compilations 

of significant scientific and technical data 

and information deemed to be of continuing 

reference value. NASA’s counterpart of peerreviewed formal professional papers but has less 

stringent limitations on manuscript length and 

extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific 

and technical findings that are preliminary or of 

specialized interest, e.g., quick release reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis.

• CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientific and technical conferences, 

symposia, seminars, or other meetings sponsored 

or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientific, technical, 

or historical information from NASA programs, 

projects, and mission, often concerned with 

subjects having substantial public interest.

• TECHNICAL TRANSLATION. 

English-language translations of foreign 

scientific and technical material pertinent to 

NASA’s mission.

Specialized services that complement the STI 

Program Office’s diverse offerings include creating 

custom thesauri, building customized databases, 

organizing and publishing research results...even 

providing videos.

For more information about the NASA STI Program 

Office, see the following:

• Access the NASA STI program home page at 

<http://www.sti.nasa.gov>

• E-mail your question via the Internet to 

<help@sti.nasa.gov>

• Fax your question to the NASA STI Help Desk 

at 443 –757–5803

• Phone the NASA STI Help Desk at 

443 –757–5802

• Write to:

NASA STI Help Desk

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076–1320
National Aeronautics and

Space Administration

IS20

George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama

35812