Title                
  :HP45 Calculator program (enhanced) V1mod7
Keywords               :HREM, Wavelength, Scherzer, Resolution, hex, oct, bin
Computer               :anything with F77
Operating System       :anything with F77
Programming Language   :Fortran 77
Hardware Requirements  :CPU, terminal
Authors                :Tony Pitt, Owen Saxton, Graeme Wood, Mike O'Keefe, ...
Correspondence Address :MAOK@CSA2.LBL.GOV
                       :M.A. O'Keefe, NCEM, LBL 72-213, Berkeley, CA 94720

Description: This is a program designed to emulate a scientific calculator
operating in reverse polish mode (originally based on a HP45, but now with
many enhancements, including binary, hex, and octal numbers, and electron
microscope functions like wavelength and resolution).   The HELP command
provides one-line explanations of each command.   Commands are -

 +        -        *        /        SQRT     REP      SIN      COS      TAN
 TYPE     DEL      PI       EXP      CLR      CUBE     SQU      REC      SWOP
 SWAP     CHS      POC      ROLL     LOG      ALOG     ASIN     ACOS     ATAN
 LN       OCT      HEX      X        DISP     INT      COMS     BIN      DEC
 INV      DEG      RAD      D>R      R>D      EXIT     WAVL     KV       SCH
 OPT      RSCH     ROPT     LIMD     LIMA     STO      RCL      HELP

Exact functions of each command are easily read in the Fortran source, which
has extensive inbuilt documentation.  Extra user-defined commands are easily
added to the source at the designated place.  The program stores input numbers
in a stack, and commands operate on the top one or two of the stack members.
Expressions can be up to 80 keystrokes long and are evaluated in reverse-polish
convention.  E.g. the result of the expression 6 5+ is 11, that of 6 5/ is 1.2,
the result of 5 5+5+3/ is 5.

The calculator is entered in "radian-decimal" mode (the prompt expresses this
fact by taking the form "RAD:DEC>" on entry), but can be changed to other
modes by the commands DEG, BIN, OCT, HEX, DEC and RAD.  In radian mode the
commands SIN, COS, TAN assume that all angles are in radians; DEG puts the
calculator into degree mode, and all trig functions then assume that all angles
are measured in degrees; RAD switches the calculator back from degree mode to
radian mode.  The commands BIN, OCT, HEX and DEC are used to switch the
calculator into binary, octal, hexadecimal and decimal modes respectively.
The mode-change commands can be used within arithmetic expressions; e.g. with
the calculator in decimal mode, the command line 23hex2b+dec will place the
decimal number 23 on the stack, convert to hexidecimal mode, place the number
2b on the stack, add the top two numbers, and convert the result to decimal 66.

The commands WAVL, KV, SCH, OPT, RSCH, ROPT, LIMD, LIMA are useful in computing
quantities used in high resolution transmission electron microscopy.  The WAVL
command gives the electron wavelength in Angstroms assuming that the top number
on the stack is the accelerating voltage of the microscope in kV. The command
KV computes the voltage from the wavelength in Angstrom units.

The commands SCH and OPT compute the Scherzer defocus and "optimum" defocus
respectively, assuming that the top two numbers on the stack are the objective
lens spherical aberration coefficient Cs in mm. and the electron wavelength in
Angstroms.  The Scherzer defocus is defined as the square root of (wavelength
times Cs), and the "optimum defocus" as the square root of (wavelength times
Cs times 1.5).  E.g. the command string  400 WAVL 1.1 OPT  is used to compute
the "optimum" defocus for a 400keV microscope with a Cs of 1.1mm.

The command RSCH (Resolution at SCHerzer defocus) gives the resolution in
Angstroms corresponding to the spatial frequency at which the linear-image
CTF reaches cross-over at Scherzer defocus; the command ROPT (Resolution at
OPTimum defocus) gives the resolution in Angstroms at the spatial frequency
at which the linear-image CTF reaches the upper limit of the optimum defocus
pass-band.  The command string  400 WAVL 1.1 ROPT  will give the "structure-
image" resolution for a 400keV electron microscope with a Cs of 1.1mm.

The commands LIMD and LIMA give the "Information Limit" resolutions due to the
effects of partial temporal and spatial coherence respectively -- i.e. the
limits at which the "envelope functions" due to chromatic aberration (spread
of focus) and incident beam convergence drop to exp(-2).

LIMD is the resolution LIMit (in A) due to Delta, where delta is the spread of
focus in Angstrom units due to the combined effects of chromatic aberration,
high-voltage ripple, energy spread in the electron beam, lens current ripple,
and vertical vibration of the specimen relative to the objective lens polepiece.
LIMD is calculated from the electron wavelength (in A) and the spread of focus
in Angstrom: e.g. the expression  400 WAVL 85 LIMD  would give the spread-of-
focus resolution limit of a 400keV microscope with a delta of 85A as 1.48A.

LIMA is the resolution LIMit (in A) due to Alpha, where alpha is the semi-angle
measured in milliradian of the cone of electrons incident on the specimen.  The
value of LIMA varies with defocus and Cs, and thus requires the presence of
four parameters on the stack -- the electron wavelength (in A), Cs(mm), the
defocus(A), and alpha(milliradian).  The expression  400 WAVL 1.1 -500 .5 LIMA
calculates a convergence resolution limit of 1.27A for a 400keV microscope with
a Cs of 1.1mm focussed at an underfocus of 500A with a convergence semi-angle
of 0.5milliradian.  NOTE: Although the other three parameters may be entered in
arbitrary order, the last entry on the stack must be the value of alpha.

References: O'Keefe & Pitt, Electron Microscopy 1980, vol.1, pp.122-123.

Compilation procedure: standard F77
Linking procedure: standard
Test data: none
General comments: i/o is to Fortran unit 3, so assign this logical unit
                  to your terminal