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...N i v e fourier booklet u r s t h y school of physics o f g d b thefouriertransform whatyouneedtoknow mathematical background for senior honours modernoptics digital image analysis optical laboratory projects msc theory processing session version transform revised september contents introduction notation properties the twodimensionalfourier thethree dimensional diracdeltafunction dirac delta function theinnite comb symmetryconditions one dimensionalsymmetry two convolutionoftwofunctions simple twodimensionalconvolution correlation functions autocorrelation questions thesinc rectangular aperture gaussians differentials sines and cosines combfunction convolution theorm auto is essential to many areas including acoustics signal optics solid state scattering more generally in solution differential equations applications as diverse weather model ingtoquantumeldcalculations thefouriertransformcaneitherbeconsideredasexpansion terms an orthogonal bases set sine cosine or a shift space from rea...