In the period between '68 and the... their Nobel Prize in '79, I was pretty much involved with a series of people who were interested in three-dimensional image reconstruction in various fields, things like PET scanning, and nuclear imaging, which uses gamma rays. We used to go to meetings about this and also the man who used to attend them was Paul Lauterbur who got the Nobel Prize two years ago for MRI, because that's also three-dimensional image reconstruction, I remember. And these meetings took place at various parts of the world and I remember, very clearly, Lauterbur; and I always thought he should have a Nobel Prize, he realised that with MRI you had to have another signal from the depth at which you... did what's called plane echoing, which is a man called [Peter] Mansfield, who shared the prize with him had invented. So the... these meetings were... but in the early days before we started these meetings the Hounsfield scanner, the MI scanner was being used. Now, the first thing he did on the MI scanner because he couldn't understand Fourier analysis, an engineer; he said, very simply, 'We will just expand the density in the three-dimensional object in the cartesian... in three-dimensional array, the series of numbers. And then in the two-dimensional images, we also have a two dimension...we relate two things by a series of linear equations.' And so he tried to solve them, now, what he didn't understand was very elementary, that if you don't have... if you have too many points in your three-dimensional grid and then you... and you haven't got enough data points, you'll get ill-conditioned equations. And that means that you won't be able to solve them, and they're subject to the slightest error or amplified noise. So the first things they produced on the MI scanner were total garbage.

[Q] Yes.

And they were done... a man called, Ross... what was his name? Ross... who was his name... Ross Stevens, was in Basel at the time, so he ripped open the... he ripped open... they had an EMI scanner and found what the programme was and discovered they were using this linear... linear equation, totally wrong, hopeless programme. So they later introduced Fourier methods or the equivalent of Fourier methods. There's a... Peter Gilbert developed an R-back weighted projection, a convolution method by Ramachandran but they're all equivalent methods, it's a question of how you best do the computation. So that was an interesting episode... where you... the thing about the Fourier method is, it tells you not only how to... it tells you exactly how many views you need to solve an object to a certain degree of resolution without amplifying noise. Tony Crowther showed how a very crude criteria was also the criteria for not amplifying noise. Anyway, this was a great time and I was... I remember when the first EMI scanners were being used. By a consultant in Manchester, they were imaging the brain and I said to them, 'Why do... why don't you...' to Hounsfield, 'Why don't you image something simple?' He said, 'What?', I said, 'A screwdriver or a pen', because then you can see, what, you know, that in mathematics, you say it's the point response function. But if you did elementary optics at school you have a pin and you actually follow what happens to the pin.

[Q] Yes.

The tail of the pin, and so they actually did, in the end, image a... not a screw driver, but a steel rod and of course, you could see the diffraction ripples and so on. But they didn't know and they... they weren’t... well, Hounsfield didn't understand optics and certainly the consultant at the Manchester didn't understand it either. So it wasn't much use what they were doing but you could calculate the point response function. And we published some papers in 1972 on this, on the point response function together with Linda Amos and Tony Crowther, so it was great. It was quite interesting because I could actually use mathematics which I always... but, I said earlier, I'm not really a mathematician, I'm doing what people in Cambridge would rather call... look down on it, applicable mathematics. The mathematics which you put to an end, you see, you might call it mathematical physics or whatever... so that was it. So that was my... but, this... this went on for a few years until we... until we got established. But the simple criteria of how you proved these things, the question of noise, whether you put in Wiener filtering and things of that sort, all that. But I... but, I... so this occupied me from 1968 to about 1974.