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|
Starts dribbling to session.out (2006/7/5, 20:11:29).
(%i2)
dist(z):=(MATRIX([1,z],[0,1]))$
(%i3) lens(f):=(MATRIX([1,0],[-1/f,1]))$
(%i4)
abcd(optics_system):=block([tmp:MATRIX([1,0],[0,1])], (for i:1 thru length(optics_system) do tmp:optics_system[i].tmp ), return(tmp))$
prop(q0,abcd):=(abcd[1][1]*q0+abcd[1][2])/(abcd[2][1]*q0+abcd[2][2])$
(%i6)
wr2q(w,r):=1/(1/r-%I*lamb/%PI/(w^2))$
(%i7) q2w(q):=sqrt(-lamb/%PI/imagpart(1/q))$
(%i8) q2r(q):=block([rp:(realpart(1/q))],
(if (rp = 0)
then
(print("#dbg: R=1/0, will substitute R with something big"),
return(1e100))
else
return(1/rp)
)
) $
(%i9)
/* find q0 for such q */
q2w0(q):=block([w,r,w0],
w:q2w(q),r:q2r(q),
w0:(w/sqrt(1+(%Pi*w^2/lamb/r)^2)),
return (w0)
)$
(%i10) q2z0(q):=block([w,r],
w:q2w(q),r:q2r(q), return(r/(1+(lamb*r/%Pi/w^2)^2))
)$
(%i11) q2q0(q):=%I*%Pi*q2w0(q)^2/lamb$
(%i12)
q0f2z_for_colim_lens(q0,f):=f+%Pi*q2w(q0)^2/lamb$
(%i13)
qf2colim_lens_posit(qstart,f):= block([q0,z0,zd],
q0:q2q0(qstart),
z0:q2z0(qstart),
zd:q0f2z_for_colim_lens(q0,f),
return(zd-z0)
)$
(%i14)
check_real(x):=if featurep(x[1],real) then if featurep(x[2],real) then if featurep(x[3],real) then true else false $
(%i15)
check_posit(x):=if (part(x[1],2)>0) then if (part(x[2],2)>0) then if (part(x[3],2)>0) then true else false $
(%i16)
check_sm1(x):=if (part(x[1],2)<ltotal) then if (part(x[2],2)<ltotal) then if (part(x[3],2)<ltotal) then true else false $
(%i17)
select_realsolutions(x):=block([temp:[]], for i:1 thru length(x) do (if check_real(x[i]) then temp:float(append(temp,[x[i]])) ), return(temp) ) $
select_posit_solutions(x):=block([temp:[]], for i:1 thru length(x) do (if check_posit(x[i]) then temp:float(append(temp,[x[i]])) ), return(temp) ) $
select_sm1_solutions(x):=block([temp:[]], for i:1 thru length(x) do (if check_sm1(x[i]) then temp:float(append(temp,[x[i]])) ), return(temp) ) $
/*=========================================================*/
/*
match one Gauss beam parameter q0(w0,r0)
to another one qf(wf,qf)
with the help of two known lens.
distance between q0 and qf is 'ltotal'
q0>|----z1-----(f1)------z2-------(f2)------z3--------|>qf
^ ^
|-------------------ltotal-------------------------|
the system should looks like above.
*/
/*=========================================================*/
qffql2z1z2z3(q0,f1,f2,qf,ltotal):=block(
[
m1,m2,m3,m4,m5,z1,z2,z3,
optics, mfull,
q0r,qoi, qfr,qfi,
eqt,eq1,solut,
eq1,eq2,eq3,
eqn1, eqn2,eqn3,
eqnev1, eqnev2, eqnev3,
slt, rsol
],
m1:dist(z1),
m2:lens(f1),
m3:dist(z2),
m4:lens(f2),
m5:dist(z3),
optics:[m1,m2, m3, m4, m5],
mfull:abcd(optics),
eqt:qf=prop(q0,mfull),
q0r:float(realpart(q0)),
q0i:float(imagpart(q0)),
qfr:float(realpart(qf)),
qfi:float(imagpart(qf)),
eq1:ev(eqt, q0=q0r+q0i*%I, qf=qfr+qfi*%I),
solut:solve([eq1], [z3]),
eqn1:imagpart(solut[1]),
eqn2:realpart(solut[1]),
eqn3:z1+z2+z3=ltotal,
eqnev1:ev(eqn1,numer),
eqnev2:ev(eqn2,numer),
eqnev3:ev(eqn3,numer),
slt:solve([eqnev1,eqnev2,eqnev3],[z1,z2,z3]),
print("slt=",slt),
rsol:select_realsolutions(slt),
rsol:select_posit_solutions(rsol),
rsol:select_sm1_solutions(rsol),
print("rsol=",rsol),
return(rsol)
);
(%o20) qffql2z1z2z3(q0, f1, f2, qf, ltotal) :=
block([m1, m2, m3, m4, m5, z1, z2, z3, optics, mfull, q0r, qoi, qfr, qfi, eqt,
eq1, solut, eq1, eq2, eq3, eqn1, eqn2, eqn3, eqnev1, eqnev2, eqnev3, slt,
rsol], m1 : dist(z1), m2 : lens(f1), m3 : dist(z2), m4 : lens(f2),
m5 : dist(z3), optics : [m1, m2, m3, m4, m5], mfull : abcd(optics),
eqt : qf = prop(q0, mfull), q0r : float(realpart(q0)),
q0i : float(imagpart(q0)), qfr : float(realpart(qf)),
qfi : float(imagpart(qf)), eq1 : ev(eqt, q0 = q0r + q0i %I,
qf = qfr + qfi %I), solut : solve([eq1], [z3]), eqn1 : imagpart(solut ),
1
eqn2 : realpart(solut ), eqn3 : z1 + z2 + z3 = ltotal,
1
eqnev1 : ev(eqn1, numer), eqnev2 : ev(eqn2, numer), eqnev3 : ev(eqn3, numer),
slt : solve([eqnev1, eqnev2, eqnev3], [z1, z2, z3]), print("slt=", slt),
rsol : select_realsolutions(slt), rsol : select_posit_solutions(rsol),
rsol : select_sm1_solutions(rsol), print("rsol=", rsol), return(rsol))
(%i21) /*=========================================================*/
/*
Zero ewaste to zero waste transformatin with lense
q0|------------(f)-----------|qf0
^ ^ ^
|----z--------| |
| |
|-------------l------------|
we are lookking for z1,l
*/
q0fq02z1(q0,f,qf):=block([f0,z1,w0tmp:q2w(q0),wftmp:q2w(qf)],
f0:%Pi*w0tmp*wftmp/lamb,
z1:f+w0tmp/wftmp*sqrt(f^2-f0^2),
return(z1)
)$
(%i22) q0fq02z2(q0,f,qf):=block([f0,z2,w0tmp:q2w(q0),wftmp:q2w(qf)],
f0:%Pi*w0tmp*wftmp/lamb,
z2:f+wftmp/w0tmp*sqrt(f^2-f0^2),
return(z2)
)$
(%i23) q0fq02l(q0,f,qf):=q0fq02z1(q0,f,qf)+q0fq02z2(q0,f,qf)$
(%i24) /*=========================================================*/
/*
for back propogation we need to change R -> -R
*/
q2bq(q):=wr2q(q2w(q),-q2r(q));
(%o24) q2bq(q) := wr2q(q2w(q), - q2r(q))
(%i25) /*=========================================================*/
/*=========================================================*/
/*=========================================================*/
/*=========================================================*/
/*=========================================================*/
/* lets solve final waste to parrallel beam,
(actually back propogation)
*/
/*=========================================================*/
/*
this code tryes to find configuration of 3 given lenses with focal
length f1,f2, f_col
in such a way that starting from with initial waste (w0)
and radius (r0)
after propogation through lens 1 (f1 focal length)
and 2 (f2 focal length)
we have a collimated region with length (dist_betw_f2_f_col)
and then after passing through the lense 3 we at some distance
match to the final waste and radius (wend, rend).
Total distance between starting and final lense position will be
calculated in to the 'ltotal'
Beam have a wave length 'lamb'.
Everything calculated in meters.
*/
/*======== Initial condition ==============================*/
ltotal:4.85$
(%i26) lamb:1.064e-6$
(%i27) /* starting waste */
w0:0.30e-3$
(%i28) r0:1e100$
(%i29) /* final waste */
wend:37.09e-6$
(%i30) rend:1e100$
(%i31)
/* lenses focal length */
f1:.025$
(%i32) f2:.075$
(%i33) f_col:0.7118$
(%i34)
/* collimated region size */
dist_betw_f2_f_col:.30$
(%i35) /*=========================================================*/
optics_after_parral_beam:[lens(-.111),dist(.05)]$
(%i36)
q0:ev(wr2q(w0,r0),numer)$
(%i37) qend:wr2q(wend,rend)$
(%i38) /*
qf:prop(qend,abcd(reverse(optics_after_parral_beam)))$
float(realpart(qf))$
float(imagpart(qf))$
*/
qf:qend$
(%i39)
/*finally position of collimated lens */
z_col:float(qf2colim_lens_posit(qf,f_col))$
Division by 0
#0: q2w(q=1/(1.0E-100-773.4423732003382*%I/%PI))
#1: q2w0(q=1/(1.0E-100-773.4423732003382*%I/%PI))
#2: q2q0(q=1/(1.0E-100-773.4423732003382*%I/%PI))
-- an error. Quitting. To debug this try debugmode(true);
(%i40) if (z_col <0)
then (print("it is not possible to get collimated beam z_col=",z_col),
quit()
) $
Maxima was unable to evaluate the predicate:
z_col < 0
-- an error. Quitting. To debug this try debugmode(true);
(%i41) qf:prop(qf,abcd([dist(z_col),lens(f_col)]))$
(%i42)
qf:prop(qf,abcd([dist(dist_betw_f2_f_col),lens(f2)]) )$
(%i43)
/* below something wrong */
dist2waste:ev(-q2z0(qf),numer)$
Division by 0
#0: q2w(q=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
#1: q2z0(q=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
-- an error. Quitting. To debug this try debugmode(true);
(%i44) rad_now:ev(q2r(qf),numer)$
(%i45) qf:ev(q2q0(qf),numer)$
Division by 0
#0: q2w(q=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
#1: q2w0(q=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
#2: q2q0(q=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
-- an error. Quitting. To debug this try debugmode(true);
(%i46) /*===========================================*/
space_between_wastes:ev(q0fq02l(q0,f1,qf), numer)$
Division by 0
#0: q2w(q=1/(1.0E-100-11.82222222222223*%I/%PI))
#1: q0fq02z1(q0=1/(1.0E-100-11.82222222222223*%I/%PI),f=0.025,qf=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
#2: q0fq02l(q0=1/(1.0E-100-11.82222222222223*%I/%PI),f=0.025,qf=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
-- an error. Quitting. To debug this try debugmode(true);
(%i47) dist2first_lens:ev(q0fq02z1(q0,f1,qf),numer)$
Division by 0
#0: q2w(q=1/(1.0E-100-11.82222222222223*%I/%PI))
#1: q0fq02z1(q0=1/(1.0E-100-11.82222222222223*%I/%PI),f=0.025,qf=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
-- an error. Quitting. To debug this try debugmode(true);
(%i48) dist2first_lens_tmp:ev(q0fq02z2(q0,f1,qf),numer)$
Division by 0
#0: q2w(q=1/(1.0E-100-11.82222222222223*%I/%PI))
#1: q0fq02z2(q0=1/(1.0E-100-11.82222222222223*%I/%PI),f=0.025,qf=((MATRIX([1,0],[-13.33333333333333,1]) . MATRIX([1,0.3],[0,1]) . MATRIX([1,0],[0,1]))[1][1]*((MATRIX...)
-- an error. Quitting. To debug this try debugmode(true);
(%i49)
z1:ev(dist2first_lens,numer)$
(%i50) z2:ev(space_between_wastes+dist2waste,numer)$
(%i51) z3:ev(z2+dist_betw_f2_f_col,numer)$
(%i52)
ltotal:z3+z_col$
(%i53)
/*
qf:wr2q( -q2r(qf), q2w(qf) )$
*/
/*
rsol:qffql2z1z2z3(q0,f1,f2,qf,ltotal-z_col)$
print("rsol=",rsol),
*/
with_stdout("answ.txt",
print("##########################################"),
print( "lambda=",lamb),
print( "Ltot=", ltotal),
print( "r0=", r0),
print( "w0=", w0),
print(),
print( "lns1.abcd=abcd_lens(", f1 , ")" ),
print( "lns1.x=", z1 ),
print( "lns2.abcd=abcd_lens(", f2 , ")" ),
print( "lns2.x=", (z2) ),
print( "lns3.abcd=abcd_lens(", f_col , ")" ),
print( "lns3.x=", (z3) ),
print("wf=", wend),
print("rf=", rend),
/*
qfinal:prop(q0,ev(mfull)),
wfinal:float(q2w(qfinal)),
rfinal:float(q2r(qfinal)),
print("#final waste=", wfinal),
print("#I was aiming to final waste"),
print("#final radius=", rfinal),
print("#I was aiming to final radius"),
*/
print("##########################################")
)$
(%i54) system("cat answ.txt")$
(%i55) system("xterm -e octave abcd.m") $
(%i56)
quit()$
|
