Instrumental analysis exam 1

Signal to noise ration
Mean/Standard Deviation
Thermal (Johnson) Noise
•Not frequency dependent (white noise)
•Vrms=Sqrt[4kTRdF]

•Also dF=1/3 tr(rise time)

Shot Noise
•Caused by charged particles crossing pn barriers or arriving at an interface

•Since electron flow is quantized at one instant there may be more quanta and another there may be less. The signal is the average of this
•irms= Sqrt[2 I e deF]
I: average current e: charge on an electron
•Can only be reduced by reduction in bandwidth
•Frequency independent

Flicker Noise
•Ubiquitous and not really explainable
• Magnitude inversely proportional to frequency

• Source flicker noise: Caused by variation in variables the control source readiation (Power, vibration,temp)
•Transmission flicker noise: Fluctuation in transmission character of sample containers
•Analyte flicker noise: Caused by fluctuation in the sample presentation system
•Significant at frequencies below 100 mhz

Environmental Noise
•Caused by interference from surroundings
•Power lines at 60 hz; Radio, TV, elevators
•Quiet region between 10^2 and 10^6
Grounding and Shielding
•Surround instrument in a conducting material that is grounded and absorbs radiaton
Difference amplifier
•removes noise by subtracting the difference between a reference input and the signal input.
•Good for removing drift noise, power line noise
Analog Filters
•Filter out noise at a different frequency from signals
• Low pass filter: allows only low frequencies to pass
•High Pass filter: allows only high frequency signals to pass
•Band Pass Filter: Allows only a particular range of frequencies to pass
Modulation
•Shift the signal to a frequency region with less noise
•Source modulation: modulate at radiation source ->Source chopper
•Sample modulation:Sample alternatively presented to the system
•Wavelength modulation:Wavelength is repeatedly varied over a wavelength range

•Also can alter some property of carrier wave signal so that the carrier wave encodes signal information

Lock-In amplifier
•Used to extract signal that is engulfed by noise
•Uses a reference signal to lock in to a signal at a specific frequency
•Reference signal must have same frequency and fixed phase relationship
Ensemble Averaging
•Numerous data sets of the same sample are collected and averaged
•In order for this to be effective, data must be sampled at a rate that is at least twice the frequency of the highest frequency component of the waveform->Nyquist frequency

• S/N= Sqrt[n] (Si/Ni)

Boxcar Averaging
•Averages a small number of adjacent points
Fourier Transform
Convert time domain to frequency, filter out noise convert back to time domain
Slit Diffraction
m lambda=d Sin[Theta]
REfractive index
Ni= C/Vi
Refraction
Change in direction of light passing through a medium

Sin[Theta1]/Sin[Theta2]=n2/n1

Scattering
Light going through matter results in momentary absorbtion of photons by atoms followed by reemission

•Rayleigh Scattering: Scattering by by molecules smaller than the wavelength of radiation-> no net energy change

•Tyndall Effect: Scattering by large molecules

•Raman Scattering:Results in a change of frequency due to vibrational energy level transitions

Electronic States:
•Singlet: no unpaired electrons
•Triplet: Two unpaired
Components of optical instrumentation
•Source of radiant energy
•Sample holder
•Wavelength Selector
•Radiation detector
•Processor/readout
Incandescent lamps
•Continuum source
•Spectral distribution described by blackbody equations
• Tungsten lamps: Visible range, near IR
Arc lamp
•Continuum source
•Xenon : Uv visible range
• Deuterium or hydrogen lamp: true continuum from 160 nm out to visible
Nernst glower
•Continuum source
• Visible to far IR range
•Semiconductor material that is heated
Globar
•Silicon carbide rod
• Range: IR to far IR
Low pressure arc lamp
•Line source
•Hollow cathode tube with metal anode, emits radiation characteristic of the metal (AA)
Lasers
Light amplification by stimulated emission of radiation
•Lasers work by:
•Pumping: light or electronic source excites the active medium
•Spontaneous emission: Active medium emits radiation randomly
•Stimulated emission: active medium gives off radiation of the same wavelength that is colliding with it and in the same direction
•Absorption: active medium absorbs radiation and becomes excited
•Population inversion: when the number of species undergoing stimulated emission is larger than the number undergoing absorption-> when there are more species in the excited state than in the lower energy state
•Line source
Interference filter
•Filters light from interference of radiation
•Filtered wavelength can be selected based on thickness of dielectric material between two mirrors
• lambda=2 d Ni/n Ni:refractive index of dielectric

•Useful for Uv vis, and IR regions

•effective bandwidth is 1.5% of peak transmitted wavelength

Free Spectral range
Range of wavelengths around chosen wavelength about which no other wavelength of radiation overlaps
Absorption filters
•Absorb certain wavelengths with colored glass or dye
• Effective bandwidth of 30 nm- 250 nm
Monochromator: Makeup
Composed of:
Entrance Slit
Collimating lens
dispersion element
focus lens
exit slit
Monochromator: Gratings:types
•Echellette n lambda=d(Sin[i]+Sin[r])
d: distance between gratings i:angle of inference r: angle of diffraction

•Echelle Grating: n lambda=2 d Sin[i]

Monochrometer: Gratings: performance
•Resolving power R: limit of a gratings ability to seperate adjacent images
R=mN m: order N: total number of grooves

•Dispersion: ability of a monochrometer to separate different wavelengths-> reciprocal linear dispersion
D^-1= d Cos[r]/n f
f: focal length, d:distance between gratings r:angle of diffraction

•Light gather power F number:
F= f/d f: focal length d: distance between gratings

Monochrometer: Gratings: slit width
•Effective bandwidth: range of wavelengths that exit the monochrometer at a given wavelength

Lamdaeff= 1/2 Wavelength difference
Lamdaeff= w D^-1 w:exit slit width

Detectors
Should have:
• High sensitivity
• High signal to noise ratio
•Constant response over a range of wavelength
•Fast response times
•No dark current
•Signal proportional to radiant power
Photovoltaic Cell
•Radiant energy creates electron/hole pairs generating a potential difference

max absorbance 550 nm

Photodiode
Reverse biased pn junction. Photons cause promotion of electrons from valence band to conduction band
Phototubes
Photoemissive material in cathode tube emits electrons when struck by radiation.

•Can be useful from ultraviolet through visible regions

Photomultiplier tube
Much more sensitive to emitted photons
•Fast response time
•Can be damaged by bright light
Charge coupled devices
•Formed from p type silicon, electrons formed from absorption of radiation collect in a potential well below the electrode.
•Charge under electrode accumulates during scan and can be measured
Thermocouple
A pair of junctions between two dissimilar metals. A voltage is generated by the difference in temperature between the junction metals
Bolometer (Thermistor)
As temperature increases valence band electrons are promoted to the conduction band which decreases resistance and increases conductivity
Pyroelectric transducer
•Special dielectric material that is polarized by an external magnetic field but remains polarized in a temperature dependent manner after the field is removed.
•Heating the material results in a change in charge distribution and a measurable current in a circuit
•Most common detector in FTIR
IR
1 micron
Visible light
400nm-650 nm
Photoconductor
•Semiconductor: acts as light dependent resistor