OGIP Memo OGIP/93-001
Specification of Physical Units within OGIP FITS files
NASA/GSFC,
Greenbelt,
MD 20771
Version: 1995 May 04
SUMMARY
A list of character strings specifying the basic physical units
used within OGIP FITS files is given.
Rules and guidelines on the construction of compound
units are also outlined.
|
This version conforms to the OGIP FITS Working Group Recommendation R5.
LOG OF SIGNIFICANT CHANGES
Release | Sections Changed | Brief Notes |
Date | ||
1993 Jan 13 | First (internal) Draft | |
1993 May 11 | All | Major revision to all strings |
1993 Aug 04 | All | Voted on as OFWG Recommendation R5. |
1994 Nov 18 | All | Made compatible with LaTeX2HTML software |
1995 May 04 | 4 | Section Added |
INTRODUCTION
In order to facilitate the use of FITS datasets by downstream s/w and users, it is clearly highly preferable that a common set of character strings are used throughout all files and software to specify the physical units in which the data are stored. This memo lists those current approved for use within the OGIP and should be strictly adhered to1.
In Section 2 we give a list of character strings specifying the basic physical units allowed within OGIP FITS files, including guidelines on the use of decimal multiples and submultiples of units. Section 3 provides a number of rules and guidelines on the construction of compound units, and a number of examples are given in Section 5. It should be noted that within the framework provided here, the ultimate responsible for choosing sensible and convenient unit strings lies with authors of FITS datasets.
Any comments or suggestions (especially if you have a requirement
for units not covered my this memo) should be
be e-mailed to the authors (LHEAVX::GEORGE
and/or
LHEAVX::ANGELINI
).
BASIC UNITS
In line with IAU recommendations, SI units should be adopted for all physical quantities with the exception of a small number of special units more convenient for astronomy. The character strings specifying the basic units allowed for use within the OGIP are listed in Tables 1 & 2, along with the allowed prefixes for multiples and submultiples listed in Table 3. Note that all strings are CASE SENSITIVE.
When used as the value of the TUNITnnn keyword in the header of a FITS extension, it is recommended that the first character of the string is placed immediately after the opening quote in the value field (i.e. placed in column 12 of the 'card image').
IAU-recommended Units
Table 2.1 lists the 7 base SI units regarded as
dimensionally independent and 2 supplementary units for plane and solid
angles, along with the 15 derived units (formed by combining base
and supplementary units) with unique symbols recognized by the IAU.
All units are given for completeness, though several are likely to be of
little use to X- and -ray astronomy.
It can be seen that in the majority of cases, the character string is
identical to the IAU-recognized symbol for the
quantity2.
The only exception is
electric resistance (with symbol
, but string
ohm
).
Finally it should be noted that despite IAU recommendations, the
measurement of plane angles in radians may often be considered inconvenient
within astronomy. Thus the use of decimal degrees is also
allowed (e.g. Table 2.2).
Quantity | Unit | Meaning | Notes |
String | |||
SI base & supplementary units | |||
length | m |
metre | |
mass | kg |
kilogram | |
time | s |
second of time | (incl sidereal time if appropriate) |
plane angle | rad |
radian | (but see text) |
solid angle | sr |
steradian | |
temperature | K |
kelvin | |
electric current | A |
ampere | |
amount of substance | mol |
mole | |
luminous intensity | cd |
candela | |
IAU-recognized derived units | |||
frequency | Hz |
hertz | s![]() |
energy | J |
joule | N m |
power | W |
watt | J s![]() |
electric potential | V |
volts | J C![]() |
force | N |
newton | kg m s![]() |
pressure, stress | Pa |
pascal | N m![]() |
electric charge | C |
coulomb | A s |
electric resistance | ohm |
ohm | V A![]() |
electric conductance | S |
siemens | A V![]() |
electric capacitance | F |
farad | C V![]() |
magnetic flux | Wb |
weber | V s |
magnetic flux density | T |
tesla | Wb m![]() |
inductance | H |
henry | Wb A![]() |
luminous flux | lm |
lumen | cd sr |
illuminance | lx |
lux | lm m![]() |
Additional Astronomical Units
Quantity | Unit | Meaning | Notes | |
String | ||||
plane angle | deg |
degree of arc |
![]() |
|
arcsec |
second of arc |
![]() |
||
arcmin |
minute of arc |
![]() |
||
time | min |
minute | (incl sidereal time if appropriate) | |
h |
hour | (incl sidereal time if appropriate) | ||
d |
day |
![]() |
||
yr |
year (Julian) |
![]() |
||
energy | ![]() |
eV |
electron volt |
![]() |
erg |
erg | ![]() |
||
length | angstrom |
angstrom | ![]() |
|
AU |
astronomical unit |
![]() |
||
lyr |
light year |
![]() |
||
![]() |
pc |
parsec |
![]() |
|
events | count |
counts | ||
photon |
photons | |||
flux density | ![]() |
Jy |
jansky | ![]() ![]() ![]() |
mag |
(stellar) magnitude | (see text) | ||
![]() |
Crab |
`crab' | (see text) | |
magnetic field | G |
gauss | ![]() |
|
area | pixel |
(image/detector) pixel | ||
barn |
barn | ![]() ![]() |
||
Miscellaneous 'units' | ||||
chan |
(detector) channel | |||
bin |
numerous applications | (including the 1-d analogue of pixel) | ||
voxel |
3-d analogue of pixel | |||
byte |
(computer) byte | |||
![$\dag $](img10.gif)
Unfortunately, a number of the IAU-recommended units listed in
Table 1 are somewhat inconvenient for some astronomical applications.
Thus Table 2 lists the OGIP-recommended
strings for such quantities.
Again, in most cases the character string is identical
to the IAU-recognized symbol for the quantity.
The only exceptions are:
- degrees of arc (with symbol
, but string
deg
) - angstrom (with symbol Å,
but string
angstrom
so as not to be confused with ampere,A
). - the character string
yr
is preferred over the IAU-recognized symbol (a) since it is the same as the symbol used for this quantity in most astronomical journals, and in common usage. arcsec
&arcmin
since the symbols ofand
may lead to confusion
Finally the `crab' was commonly used in the early days of X-ray astronomy, and is represented in Table 2. However this unit (or more commonly the `millicrab') should be avoided wherever possible as the conversion to more standard specifications of flux density is a function of the spectrum of the source (relative to that of the Crab). Strictly speaking, the same is true regarding the use of stellar `magnitudes' (
mag
).
Prefixes for Multiples & Submultiples
The IAU-approved list of prefixes to note decimal multiples and
submultiples of units are listed in Table 3, along with the
corresponding character strings.
It can be seen that the character is
the same as the IAU-approved symbol for the prefix with the
exception of micro (), which has the symbol
,
but character
u
.
However, with the exception of centi (),
the OGIP strongly recommends the use of
prefixes which are powers of 3.
Thus strings
to specify decimal multiples & submultiples of the units given in
Table 1
can be formed3by preceeding the listed character string by the
relevant prefix character from Table 3.
Decimal multiples & submultiples of the units listed in Table 2
should NOT used, with the exception of
electron volt (eV
),
jansky (Jy
),
parsec (pc
), and
crab (Crab
, for which millicrab, mCrab
ONLY is allowed).
Compound prefixes (e.g. ZYerg
for erg) should never be used.
The result is regarded as a single unit string when constructing
compound units (see Section 3).
It should be noted that the use of these standard prefixes
greatly increases the case sensitivity of the resultant string.
RULES FOR CONSTRUCTION OF COMPOUND UNITS
The rules and syntax for the construction of compound units are fairly straightforward, involving standard characters preceeding or following the string specifying each component unit.
Throughout this section, the symbols str1
, str2
etc. are
used to denote strings conforming to the rules given in Section 2 to
specify physical units.
Basic Syntax
A compound unit is considered to be formed by a series of sub-strings of
component units & mathematical operations. Each of these sub-strings
must be separated by at least one space or a mathematical operator
(*
or /
).
In line with the rules given below, all such
sub-strings should be considered in a multiplicative sense unless
beginning with a slash (/
), or enclosed within one or more
pairs of brackets.
Multiplication
Multiplicative units can be specified either:
- by simply using one or more preceeding spaces
e.g.'str1 str2'
(The recommended method) - by the use of a single asterix (
*
) with or without one or more spaces on either side
e.g.'str1 * str2'
(This syntax should never be used preceeding a sub-string which starts with a slash - see Section 3.1.2).
Division
Units which form the denominator of a compound expression can be
specified either:
- by using a slash (
/
) with or without one or more spaces on either side
e.g.'str1 /str2'
or'str1 / str2'
or'str1/str2'
If such a syntax is used, it is recommended that no space is included between the slash and the unit string. - by raising a multiplicative unit to a negative power (see below)
e.g.
'str1 /str2 str3'
is equivalent to 'str1 str3 /str2'
whilst
'str1 /str2 /str3'
is equivalent to 'str1 /(str2 * str3)'
Raising to Powers
A unit string raised to the power y
is specified
- by using two asterixes (
**
) followed by the index enclosed within round brackets and with no preceeding or intervening spaces. e.g.'str1**(y)'
or'str1**(-y)'
However, ify
is positive, then the brackets need not be included, but a following space is recommended if additional sub-strings follow.
The use of brackets
Any number of pairs of round brackets ()
may be used within
the string for a compound unit in order to prevent ambiguities.
As described within this section, a number of rules always/often require
their use.
However, it is suggested that conservative use is made of such
pairs of brackets in order to minimise the total length of compound
strings. (It should be remembered that a maximum of 68 characters
are allowed in the card image of keywords.)
Avoidance of underflows & overflows
The inclusion of numerical factors within the unit string should generally be avoided (by the use of multiples and/or submultiples of component basic units; Section 2.3).
However, occasionally it may be preferable to include such factors on the grounds of user-friendliness and/or to minimise the risk of computer under- or overflows. In such cases, the numerical factor can simply be considered a basic unit string and all rules & guidelines given in Section 2 apply.
It should be remembered, however, that the use of numerical (scaling) factors within the unit string can result in additional overheads in the parsing/interpretation of the string if the string is used for any purpose other than as a 'label'. The inclusion of numerical factors should therefore be avoided wherever possible, and should never replace the use of the TSCALnnn keyword.
The following additional guidelines are suggested:
- the numerical factor should precede any unit strings
- only powers of 10 are used as numerical factors
A prime example is astronomical luminosities, and examples of this case along with a number of more complex examples is given in Section 4.
Mathematical Operations & Functions
The character strings denoting mathematical operations are listed in Table 4. It should be noted that the (round) brackets are mandatory in all cases in which they are included in the table (with the exception of raising units to positive powers - see Section 3.1.3).
String | Meaning |
str1 * str2 |
Multiplication (see also Section 3.1.1) |
str1 /str2 |
Division (see also Section 3.1.2) |
str1**(y) |
Raised to the power y
(see also Section 3.1.3) |
log(str1) |
Common Logarithm (to base 10) |
ln(str1) |
Natural Logarithm |
exp(str1) |
Exponential (![]() |
sqrt(str1) |
Square root |
sin(str1) |
Sine |
cos(str1) |
Cosine |
tan(str1) |
Tangent |
asin(str1) |
Arc Sine |
acos(str1) |
Arc Cosine |
atan(str1) |
Arc Tangent |
sinh(str1) |
Hyperbolic Sine |
cosh(str1) |
Hyperbolic Cosine |
tanh(str1) |
Hyperbolic Tangent |
RULES FOR QUANTITIES WITH NO OR UNKNOWN UNITS
The following rules apply:
- If the physical quantities are dimensionless, then a blank string should
be used. (The string
NONE
, used in some ROSAT files is deprecated). - If the units of a physical quantity are unknown, then the (case-sensitive)
string
UNKNOWN
should be used.
UNKNOWN
.
EXAMPLES
For illustration, example strings representing a number of compound units are given below, along with a limited number of alternatives. It should be noted that within the rules given in Section 3, the number of spaces between individual unit sub-strings is left a matter for personal preference.
- STRING =
'count /s'
(recommended)
Meaning: counts per second
Alternatives:
STRING ='count/s'
STRING ='count s**(-1)'
STRING ='count / s'
STRING =' count /s '
(discouraged) - STRING =
'/pixel /s'
(recommended)
Meaning: per pixel per second
Alternatives:
STRING ='/(pixel * s)'
- STRING =
'count /m**2 /s /eV'
(recommended)
Meaning: counts per square metre per second per electron volt
Alternatives:
STRING ='count m**(-2) * s**(-1) * eV**(-1)'
STRING ='count /(m**2 * s * eV)'
- STRING =
'erg /pixel /s /GHz'
(recommended)
Meaning: ergs per pixel per second per gigahertz
Alternatives:
STRING ='erg /s /GHz /pixel'
STRING ='erg /pixel /(s * GHz)'
(discouraged) - STRING =
'keV**2 /yr /angstrom'
(recommended)
Meaning: square kiloelectron volts per year per angstrom
Alternatives:
STRING ='10**(10) keV**2 /yr /m'
(discouraged)
STRING ='(10**2 MeV)**2 /yr /m'
(strongly discouraged) - STRING =
'10**(46) erg /s'
(user-friendly)
Meaning:ergs per second
Alternatives:
STRING ='10**46 erg /s'
STRING ='10**(39) J /s'
STRING ='10**(39) W'
(recommended)
STRING ='10**(15) YW'
STRING ='YJ /fs'
(for the purist) - STRING =
'10**(-7) J /cm**2 /MeV'
Meaning:joules per square centimetre per megahertz
Alternatives:
STRING ='10**(-9) J m**(-2) eV**(-1)'
STRING ='nJ m**(-2) eV**(-1)'
STRING ='nJ /m**2 /eV'
(recommended) - STRING =
'sqrt(erg /pixel /s /GHz)'
(recommended)
Meaning: The square root of Example 4
Alternatives:
STRING ='(erg /pixel /s /GHz)**(0.5)'
STRING ='(erg /pixel /s /GHz)**(1/2)'
(discouraged)
STRING ='erg**(0.5) pixel**(-0.5) s**(-0.5) GHz**(-0.5)'
(discouraged) - STRING =
'log(photon /m**2 /s /Hz)'
(recommended)
Meaning: The common log of a photon flux density
Alternatives:
STRING ='log( photon /m**2 /s /Hz )'
(and those associated with the unit sub-strings) - STRING =
'sin( /pixel /s)'
(recommended)
Meaning: The sine of Example 2
Alternatives:
None (except those associated with the individual unit sub-strings) - STRING =
'(count /s) (/pixel /s)'
Meaning: Example 1 multiplied by Example 2
Alternatives:
STRING ='(count /s) * (/pixel /s)'
STRING ='count /pixel /s**2'
(recommended) - STRING =
'log(photon /cm**2 /s /Hz) /(sin( /pixel /s))'
(recommended)
Meaning: Example 9 divided by Example 10
Alternatives:
STRING ='log(photon /cm**2 /s /Hz) (sin( /pixel /s))**(-1)'
(discouraged)
ACKNOWLEDGMENTS
We would like to thank the numerous people who have contributed valuable comments to the various drafts of this memo, and in particular Don Wells, Clive Page, Bill Pence & Jonathan McDowell.
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- SUMMARY
- LOG OF SIGNIFICANT CHANGES
- INTRODUCTION
- BASIC UNITS
- RULES FOR CONSTRUCTION OF COMPOUND UNITS
- RULES FOR QUANTITIES WITH NO OR UNKNOWN UNITS
- EXAMPLES
- ACKNOWLEDGMENTS
- USEFUL LINKS TO OTHER HTML PAGES
- About this document ...
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