## 2 Literature Review
### Combining the Geometries  
#### 2.3.1 Confocal Microscopy  
Historically, the first approach to combine conventional and scanning imaging techniques was confocal microscopy. The principle of confocal microscopy is illumination by a spot of light and detection of the light coming from a small _confocal_ region of the object using a lens focused on a pinhole in front of a detector. Confocal microscopy has two main advantages over conventional microscopy. First, the pinhole rejects light that comes from anywhere other than the confocal spot. Not only does this remove background, stray light, it also filters out light from defocused regions of the object, giving rise to an optical sectioning property. Second, the overall PSF, \(H\), for the confocal system is given by the product of the PSFs for the illumination and the detection systems, resulting in, in principle, an improved resolution [5]:  
\[H(v)=H_{1}(v)H_{2}(v), \tag{2}\]  
where \(H_{1},H_{2}\) are the PSFs for illumination and detection, and the transverse optical coordinate \(v\) is defined in terms of radius \(\rho\) as \(v=2\pi\rho\sin\alpha/\lambda\), so one Airy unit 1 AU (the distance to the first dark ring of the Airy disk) corresponds to \(v\approx 3.83\). The spatial frequency cut-off is equal to the sum of the cut-offs for illumination and detection [5]. The OTF for confocal fluorescence is given by the convolution of the OTFs for the illumination and detection systems, \(C(m)=C_{1}(m)\otimes C_{2}(m)\), where \(m\) is the spatial frequency. These improvements in resolution can be explained by a trade-off of field-of-view, or after building up a complete image, by trade-off of imaging time. In 1940, [PERSON] described a system where the object was illuminated with a line of light focused from a slit and the image of the illuminated line imaged through a second slit [44]. Thus, this is basically a confocal line illumination system: imaging along the line of illumination is conventional. Actually, [PERSON]'s system was more clever than that (Figure 1). The principle of [PERSON]'s microscope is that the axes of illumination (AB) and imaging (CD) are offset by an angle of 45\({}^{\circ}\). Points along the illumination axis are imaged into a line EF at right angles to it. The imaging lens has a magnification of unity so that an aberration-free image can be formed even though the tube length varies as a result of variation in the distance from the plane of the imaging lens. The sample is illuminated by a plane of light using the slit A. A slit is placed to image light within a certain range of the axially illuminated region. Even for a finite slit width, the whole of this region is imaged without aberration. By scanning the object in the direction along AB, a depth image can be integrated. If the width of the detection slit is made very narrow, the system effectively becomes a confocal system. However, it is a confocal system with offset axes, as in the specular microscope [45], theta microscope [46], or dual-axes microscope [47]. These systems all give an enhanced optical sectioning property, as a result of angular gating [48; 49]. In the plane perpendicular to the slits, the overall PSF is given by the product of the illumination and detection PSFs. Note that the illumination plane through AB being imaged into the plane through EF is a special case of the Scheimpflug condition, valid for paraxial conditions, which states that the object plane, the image plane, and the median plane of the lens all intersect [50]. In [PERSON]'s system, the image was detected using a photographic film that was scanned beneath the slit F.  
[PERSON] described, in 1943, a microphotometer system, operating in either a transmission or reflection geometry that used a diaphragm in front of the detector to reject stray light [51]. However, the system did not seem to incorporate scanning, so it did not produce an image as such. [PERSON] carried on with their work and even published a paper in the high-impact journal _Science_[52].