TK+1 =v #1 :n :s b :c UV-VIS. SPECTROMETER with PMT DETECTOR #2 :n freq :v 7.495E14 :s o :u Hz :d Hz :c frequency (Hz) #3 :n E :v 4.96626195E-19 :s o :u Joule :d Joule :c energy (Joule, erg, eV, kcal/mole) #4 :n v :v 25000 :s o :u cm-1 :d cm-1 :c wavenumber (cm-1) #5 :n lambda :v .00004 :s i :u cm :d nm :c wavelength of light (cm, , µm, nm) #6 :n :s b :c --------MONOCHROMATOR---------- #7 :n m :v 1 :s i :c order (unitless) #8 :n d :v .0008333333333333333334 :s o :u mm :d mm :c grating constant (mm, cm, µm) #9 :n theta :v .02484918557178670462 :s o :u radians :d degrees :c rotation angle of grating (radians, degrees) #10 :n Phi :v .2617993877991494365 :s i :u radians :d degrees :c monochromator takeoff angle (radians, degrees) #11 :n alpha :v .2866485733709361411 :s o :u radians :d degrees :c incidence angle (radians, degrees) #12 :n beta :v .2369502022273627319 :s o :u radians :d degrees :c diffraction angle (radians, degrees) #13 :n lines :v 1200 :s i :u lines/mm :d lines/mm :c grating ruling density (lines/mm) #14 :n AngDisp :v 1234.493728310058664 :s o :u mm-1 :d mm-1 :c Angular dispersion (mm-1, nm-1) #15 :n LinDisp :v 370348.1184930175995 :s o :u mm/mm :d mm/nm :c Linear Dispersion (mm/mm, mm/nm, mm/) #16 :n RLD :v .000002700162225932446891 :s o :u mm/mm :d nm/mm :c Reciprocal linear dispersion (nm/mm, /mm) #17 :n Fm :v 300.0000000000000001 :s i :u mm :d mm :c Focal length on monochromator (mm, cm, m) #18 :n Sg :v .000001350081112966223445 :s o :u mm :d nm :c Geometrical spectral bandpass (mm, µm, nm, ) #19 :n S :v .000001350747779632890112 :s o :u mm :d nm :c Spectral bandpass (mm, µm, nm, ) #20 :n Snu :v 84.421736227055632 :s o :u cm-1 :d cm-1 :c Spectral bandpass (cm-1) #21 :n H :v 5 :s i :u mm :d mm :c Slit height (mm, µm) #22 :n W :v .5 :s i :u mm :d mm :c Slit width (mm, µm) #23 :n Top :v .5 :s i :c Transmission factor of monochromator #24 :n Sd :v 6.666666666666666667E-10 :s o :u mm :d nm :c diffraction limited resolution (mm, µm, nm, ) #25 :n N :v 60000 :s o :c Total number of lines in grating (unitless) #26 :n Wg :v 50 :s i :u mm :d cm :c aperture (mm, cm, m) #27 :n omega :v .02664435666941630529 :s o :u sr :d sr :c acceptance solid angle, steradians #28 :n Fnumber :v 5.429281020244886116 :s o :c F-number of monochromator #29 :n As :v .025 :s o :u cm2 :d mm2 :c Slit area (cm2, mm2) #30 :n Ap :v 2397.992100247467478 :s o :u mm2 :d cm2 :c grating area viewed from entrance slit #31 :n PhiIn :v .02347903832094512019 :s o :u watts :d watts :c Radiant power input into monochromator #32 :n Straylight :v .01 :s i :c Percent stray light #33 :n Phi0 :v .0000001487108407763642862 :s o :u watts :d watts :c Radiant power passed by monochromator #34 :n :s b :c ---------LIGHT SOURCE------------- #35 :n emisiv :v .5 :s i :c emissivity of blackbody #36 :n Tb :v 2500 :s i :u K :d K :c Temperature of blackbody (K, C) #37 :n nm :v 400 :s o :u nm :d nm :c wavelength in nm #38 :n peak :v 1158.8 :s o :u nm :d nm :c Peak wavelength (nm, , µm, cm) #39 :n B :v 35.248046875 :s o :u W/sr/cm2 :d W/sr/cm2 :c Total radiance over all wavelengths #40 :n Blambda :v .0003307253735678069984 :s o :u W/sr/nm/cm2 :d W/sr/nm/cm2 :c Source spectral radiance (W/sr/nm/cm2) #41 :n :s b :c -----PHOTOMULTIPLIER DETECTOR------------- #42 :n Klam :v .2 :s i :c Cathode quantum efficiency #43 :n g :v 3.215030076126467495 :s o :c gain per stage #44 :n SEF :v .4514611385091210115 :s o :c secondary emission factor #45 :n V :v 600 :s i :u volts :d volts :c total voltage applied #46 :n Vd :v 66.66666666666666666 :s o :u volts :d volts :c voltage per dynode (volts, KV) #47 :n k :v 9 :s i :c number of dynodes #48 :n M :v 36699.94051720203309 :s o :c multiplication factor #49 :n rt :v 1000 :s i :u sec-1 :d sec-1 :c cathode thermionic emission rate (sec-1) #50 :n eta :v .9 :s i :c collection efficiency #51 :n Rlam :v .06451532424704258704 :s o :u amps/watt :d amps/watt :c radiant cathode responsivity (amps/watt) #52 :n Flux :v 299442200740.8696721 :s o :u sec-1 :d sec-1 :c Photon flux on cathode (sec-1) #53 :n rcp :v 59888440148.17393441 :s o :u sec-1 :d sec-1 :c cathode photoelectron emission rate, sec-1 #54 :n ic :v 9.594128111737464293E-9 :s o :u amps :d amps :c cathode photocurrent (amps, mA, µA, nA, pA) #55 :n ict :v 1.602E-16 :s o :u amps :d amps :c cathode thermionic dark current (amps, mA, µA, nA, pA) #56 :n iat :v 5.29139742377018913E-12 :s o :u amps :d amps :c anode thermionic dark current (amps, mA, µA, nA, pA) #57 :n T :v 303 :s i :u K :d K :c Temperature of load resistor (K, C) #58 :n RL :v 1000 :s i :u ohms :d ohms :c Load (or feedback) resistance (ohms, Kohms, Mohms) #59 :n sigmai :v 1.644460074794777006E-9 :s o :u amps :d amps :c signal shot noise current (amps, mA, µA, nA, pA) #60 :n sigmat :v 2.124965253602803824E-13 :s o :u amps :d amps :c thermionic shot noise current (amps, mA, µA, nA, pA) #61 :n excess :v 0 :s i :u amps :d amps :c excess noise current (amps, mA, µA, nA, pA) #62 :n sigmad :v 2.124965253602803824E-13 :s o :u amps :d amps :c total dark noise current (amps, mA, µA, nA, pA) #63 :n sigma :v 1.644460088524138331E-9 :s o :u amps :d amps :c total shot noise current (amps, mA, µA, nA, pA) #64 :n sigmav :v .000001644460088524138331 :s o :u volts :d volts :c total shot noise voltage (volts, mvolts) #65 :n sigmaJ :v 2.891850618548613759E-9 :s o :u volts :d volts :c Johnson noise voltage (volts, mvolts) #66 :n flicfac :v 0 :s i :c flicker factor #67 :n sigmaf :v 0 :s o :u volts :d volts :c flicker noise voltage (volts, mvolts) #68 :n sigman :v .000001644462631241226131 :s o :u volts :d volts :c total noise voltage (volts, mvolts) #69 :n t :v 1 :s i :u sec :d sec :c integration time (sec) #70 :n DeltaF :v .5 :s o :u Hz :d Hz :c noise bandwidth, Hz #71 :n tau :v .5 :s o :u sec :d sec :c RC time constant (sec) #72 :n resptime :v 2.5 :s o :u sec :d sec :c RC response time (sec) #73 :n ia :v .0003168935379136627204 :s o :u amps :d amps :c reference photocurrent (amps, mA, µA, nA, pA) #74 :n SNR :v 192722.6721592567255 :s o :c signal-to-noise ratio of incident intensity :a SNR #75 :n :s b :c ----SAMPLE and OUTPUT SIGNAL------- #76 :n a :v 1 :s i :c absorptivity of analyte #77 :n b :v 1 :s i :u cm :d cm :c path length of cell #78 :n c :v 1 :s i :c concentration of analyte #79 :n A :v 1 :s o :c true aborbance #80 :n ias :v .00003172104314515763831 :s o :u amps :d amps :c sample photocurrent (amps, mA, µA, nA, pA) #81 :n Es :v .3169252325588515104 :s o :u volts :d volts :c reference signal voltage (volts, mvolts) #82 :n Ess :v .03172104843655506208 :s o :u volts :d volts :c sample signal voltage (volts, mvolts) #83 :n sigmas :v 5.202839261479611126E-10 :s o :c sample shot noise current (amps, mA, µA, nA, pA) #84 :n Aobs :v .9996092846037472272 :s o :c Measured absorbance #85 :n RSDref :v .00000518931400627932104 :s o :c RSD of reference signal #86 :n RSDsamp :v .00001640185424442401489 :s o :c RSD of sample signal #87 :n RSD :v .00001720319163734150843 :s o :c RSD of transmission #88 :n RSDA :v .0007469103464325931722 :s o :c Percent RSD of absorbance =u #1 :f radians :m 57.29577951308232088 :t degrees #2 :f mm :m 1000000 :t nm #3 :f mm :m 1E7 :t #4 :f mm :m .0009999999999999999999 :t m #5 :f mm :m 1000 :t µm #6 :f mm :m .1 :t cm #7 :f mm/mm :m .0000009999999999999999999 :t mm/nm #8 :f mm/mm :m .0000001 :t mm/ #9 :f mm :m 1000 :t µm #10 :f mm/mm :m 1000000 :t nm/mm #11 :f mm/mm :m 1E7 :t /mm #12 :f mm-1 :m .0000009999999999999999999 :t nm-1 #13 :f mm2 :m .01 :t cm2 #14 :f watts :m 1000000 :t µwatts #15 :f watts :m 1000 :t mwatts #16 :f cm :m 1E7 :t nm #17 :f nm :m 10 :t :c = option-shift-A #18 :f ppm :m 1000 :t ppb #19 :f ppm :m .00009999999999999999999 :t % #20 :f ml :m 1000 :t µl #21 :f g :m 1000000 :t µg :c µ = option-m #22 :f l :m 1000 :t ml #23 :f µm :m 1000 :t nm #24 :f erg :m .0000001 :t Joule #25 :f eV :m 1.6E-19 :t Joule #26 :f J :t Joule #27 :f cm :m 1E7 :t nm #28 :f nm :m 10 :t #29 :f ppm :m 1000 :t ppb #30 :f ppm :m .00009999999999999999999 :t % #31 :f ml :m 1000 :t µl #32 :f g :m 1000000 :t µg #33 :f l :m 1000 :t ml #34 :f µm :m 1000 :t nm #35 :f m :m 100 :t cm #36 :f in :m 2.54 :t cm #37 :f cm2 :m 100 :t mm2 #38 :f eV :m 23.06 :t kcal/mole #39 :f cm/sec :m 10 :t mm/sec #40 :f cm :m 1E7 :t nm #41 :f nm :m 10 :t :c = option-shift-A #42 :f ppm :m 1000 :t ppb #43 :f ppm :m .00009999999999999999999 :t % #44 :f ml :m 1000 :t µl #45 :f g :m 1000000 :t µg :c µ = option-m #46 :f l :m 1000 :t ml #47 :f µm :m 1000 :t nm #48 :f erg :m .0000001 :t Joule #49 :f eV :m 1.6E-19 :t Joule #50 :f J :t Joule #51 :f cm :m 1E7 :t nm #52 :f nm :m 10 :t #53 :f ppm :m 1000 :t ppb #54 :f ppm :m .00009999999999999999999 :t % #55 :f ml :m 1000 :t µl #56 :f g :m 1000000 :t µg #57 :f l :m 1000 :t ml #58 :f µm :m 1000 :t nm #59 :f m :m 100 :t cm #60 :f in :m 2.54 :t cm #61 :f cm2 :m 100 :t mm2 #62 :f eV :m 23.06 :t kcal/mole #63 :f C :t K :a 273 #64 :f cm-1 :m .1 :t mm-1 #65 :f cm :m 1E7 :t nm #66 :f nm :m 10 :t :c = option-shift-A #67 :f ppm :m 1000 :t ppb #68 :f ppm :m .00009999999999999999999 :t % #69 :f ml :m 1000 :t µl #70 :f g :m 1000000 :t µg :c µ = option-m #71 :f l :m 1000 :t ml #72 :f µm :m 1000 :t nm #73 :f erg :m .0000001 :t Joule #74 :f eV :m 1.6E-19 :t Joule #75 :f J :t Joule #76 :f cm :m 1E7 :t nm #77 :f nm :m 10 :t #78 :f ppm :m 1000 :t ppb #79 :f ppm :m .00009999999999999999999 :t % #80 :f ml :m 1000 :t µl #81 :f g :m 1000000 :t µg #82 :f l :m 1000 :t ml #83 :f µm :m 1000 :t nm #84 :f m :m 100 :t cm #85 :f in :m 2.54 :t cm #86 :f cm2 :m 100 :t mm2 #87 :f eV :m 23.06 :t kcal/mole #88 :f cm/sec :m 10 :t mm/sec #89 :f cm :m 1E7 :t nm #90 :f nm :m 10 :t :c = option-shift-A #91 :f ppm :m 1000 :t ppb #92 :f ppm :m .00009999999999999999999 :t % #93 :f ml :m 1000 :t µl #94 :f g :m 1000000 :t µg :c µ = option-m #95 :f l :m 1000 :t ml #96 :f µm :m 1000 :t nm #97 :f erg :m .0000001 :t Joule #98 :f eV :m 1.6E-19 :t Joule #99 :f J :t Joule #100 :f cm :m 1E7 :t nm #101 :f nm :m 10 :t #102 :f ppm :m 1000 :t ppb #103 :f ppm :m .00009999999999999999999 :t % #104 :f ml :m 1000 :t µl #105 :f g :m 1000000 :t µg #106 :f l :m 1000 :t ml #107 :f µm :m 1000 :t nm #108 :f m :m 100 :t cm #109 :f in :m 2.54 :t cm #110 :f cm2 :m 100 :t mm2 #111 :f eV :m 23.06 :t kcal/mole #112 :f C :t K :a 273 #113 :f amps :t amp #114 :f amps :t A #115 :f amps :m 1000 :t mA #116 :f amps :m 1000000 :t µA #117 :f amps :m 1E9 :t nA #118 :f amps :m 1E12 :t pA #119 :f watts :t W #120 :f watts :m 1000000 :t µwatts #121 :f watts :m 1000 :t mwatts #122 :f volts :t V #123 :f volts :m .0009999999999999999999 :t KV #124 :f volts :m 1000 :t mvolts #125 :f volts :m 1000 :t mv #126 :f sec-1 :t Hz #127 :f ohms :t ohm #128 :f ohms :m .0009999999999999999999 :t Kohms #129 :f ohms :m .0000009999999999999999999 :t Mohms =l #1 :n V :d volts :u volts :v 100 200 300 400 500 600 700 800 900 1000 E #2 :n :v E #3 :n :v E #4 :n SNR :v 99536.49391935215545 122237.2075161786834 133138.7227701048245 139751.1562428739674 144254.0815015915799 147547.2365072374048 150075.8910453479099 152087.6586427028491 153732.0548534208614 E =f =r #1 :r "Assumptions: equal entrance and exit slits, equal focal :s C #2 :r " lengths of collimator and focusing elements :s C #3 :r d=1/lines #4 :r AngDisp = m/(d*cos(beta)) #5 :r LinDisp = Fm*AngDisp #6 :r RLD=1/LinDisp #7 :r Sg=W/LinDisp #8 :r S = Sg+Sd #9 :r Snu=.1*S/(lambda*lambda) #10 :r Sd = lambda/(m*N) #11 :r N = Wg/d #12 :r beta=Phi-theta #13 :r alpha=theta+Phi #14 :r m*lambda=2*d*cos(Phi)*sin(theta) #15 :r omega=Ap/Fm^2 #16 :r Ap=Wg^2*cos(alpha) #17 :r PhiIn=B*As*omega #18 :r As=0.01*W*H #19 :r Phi0=Blambda*As*omega*Top*Sg*1e6 #20 :r Fnumber=Fm/sqrt(4*Ap/pi()) #21 :r lambda = 1/v #22 :r Blambda = emisiv*1.19111E16*nm^-5/(exp(1.438e7/(nm*Tb))-1) #23 :r E = (6.6261E-34)*freq #24 :r freq = (2.998E10)/lambda #25 :r B=emisiv*1.8047e-12*Tb^4 #26 :r peak=2.897e6/Tb #27 :r nm=lambda*1e7 #28 :r exponent=1.438e7/(nm*Tb) #29 :r LambdaT=nm*Tb #30 :r lambda = 1/v #31 :r E = (6.6261E-34)*freq #32 :r freq = (2.998E10)/lambda #33 :r M=g^k #34 :r Vd=V/k #35 :r g=0.17*Vd^.7 " this is partly empirical #36 :r rcp=Klam*Flux #37 :r Rlam=(Klam*1.602e-19)/E #38 :r ia=eta*M*Rlam*Phi0 #39 :r ic=rcp*1.602e-19 #40 :r Flux=Phi0/E #41 :r ict=rt*1.602e-19 #42 :r iat=M*eta*ict #43 :r Es=RL*((ia*Straylight/100)+ia+iat) #44 :r sigmai=sqrt(2*1.602e-19*(1+SEF)*M*ia*DeltaF) #45 :r SEF=1/(g-1) #46 :r sigmat=sqrt(2*1.602e-19*(1+SEF)*M*iat*DeltaF) #47 :r sigmad=sqrt(sigmat^2+excess^2) #48 :r sigma=sqrt(sigmad^2+sigmai^2) #49 :r sigmaJ=sqrt(4*1.38e-23*T*RL*DeltaF) #50 :r sigman=sqrt((RL*sigma)^2+sigmaJ^2+sigmaf^2) #51 :r sigmav=RL*sigma #52 :r SNR=Es/sigman #53 :r DeltaF=1/(2*t) #54 :r DeltaF=1/(4*tau) #55 :r resptime=5*tau #56 :r sigmaf=flicfac*Es #57 :r A=a*b*c #58 :r ias=(ia*Straylight/100)+ia*10^(-A) #59 :r Ess=RL*(ias+iat) #60 :r sigmas=sqrt(2*1.602e-19*(1+SEF)*M*(ias+iat)*DeltaF) #61 :r Aobs=log(Es/Ess) #62 :r RSDref=sigmai/ia #63 :r RSDsamp=sigmas/ias #64 :r RSD=sqrt(RSDref^2+RSDsamp^2) #65 :r RSDA=100*.434*RSD/Aobs =p #1 :n SNRvsVoltage :t Line chart :i "" :s Yes :z None :g No :l Linear :h "" :v "" :x V :u #1 :y SNR :f 1 :p Lines :c "*" :m 0 E =t #1 :v Vertical :s Show :f 1 :t "" :u E #2 :v Vertical :s Show :f 1 :t "" :u E =n =g #1 :c .0000009999999999999999999 :i 10 :v Yes :a Yes :r Yes :h No :t 1 %Tv,f,39,4,0,1,0