Ha! Thanks Bob and Chris! Now I've got a useful tool to correct vignetting on my pinhole (giants or minuscules)... All I need to do if install the equation on my computer, feed in the appropriate values for the "n" and "t" and churn out the outcome for "z". Then, I'll just pull out my dodging tool and dodge as appropriate, in front of the pinhole or in camera. Piece of cake, really... -:)) Best regards! Guy P.S. Hey... Did I see "z" on the right-hand side of the equation? ...-:?)) We've got to pull this guy out of of there and get it to the left, otherwise we're in trouble. Aren't we? ----- Original Message ----- From: "Bob Blakely" <Bob@Blakely.com> To: "List for Photo/Imaging Educators - Professionals - Students" <photoforum@listserver.isc.rit.edu> Sent: Sunday, August 24, 2003 3:18 AM Subject: Re: Minimizing pinhole image falloff - Correction > Damn close there! It's the integral of the cos of a sin. > > As best I can do with plain text... > > Jn(z) = 1 / pi * Integral, 0 to pi of cos[z * sin(t) - n * t] * dt > > where t is theta. > > Regards, > Bob... > -------------------------------------------- > "Do not suppose that abuses are eliminated by destroying > the object which is abused. Men can go wrong with wine > and women. Shall we then prohibit and abolish women?" > -Martin Luther > > ----- Original Message ----- > From: "Chris" <nimbo@ukonline.co.uk> > To: "List for Photo/Imaging Educators - Professionals - Students" > <photoforum@listserver.isc.rit.edu> > Sent: Saturday, August 23, 2003 2:01 PM > Subject: RE: Minimizing pinhole image falloff - Correction > > > > Thank you. > > > > We didn't do Bessel functions except in fm radio theory. The theory that > I > > don't remember involved an approximation. When I tried to do the > > integration myself just now I got the integral of the sin of a sin which I > > think is the differential form of the Bessel function. Very interesting. >
