The targets used by P.A.T. have a history and a specific mathematical explanation. They both go back to the mid nineteenth century, back when Léon Foucault contributed to their elaboration with his works. Nowadays, P.A.T. has taken this very line pattern over to popularise it and provide our customers with the best technical tools for the timing of their lenses and photo sensors with maximum simplicity.

Léon Foucault (1819-1868), who was an eminent French physician and astronomer (best known, among other things, for having invented the gyroscope, determined the speed of light, and demonstrated the Earth’s rotation, thanks to the famous experiment of Foucault pendulum), directed his initial research towards the field of photography, then later, towards the most challenging matters of the theory of light. His aim being to improve the precision of his astronomical instruments, he elaborated a tool he called a “test chart”, though he kept it for his personal use, without ever thinking of getting it registered in any way whatsoever – perhaps thinking no one would ever take any interest in his invention. It is nevertheless mentioned in Recueil des travaux scientifiques de Léon Foucault, a posthumous work published in 1878, and more precisely in the chapter “Mémoire sur la construction des télescopes en verre argenté”.

*Text resulting from the research by Aurélien Dubois, DOP.*

“However, in order to be able to come to an exact result, and to give a less approximate expression that the one usually borrowed from the common language, one must direct the mirror fitted as a Newtonian telescope towards a test-chart placed at a distance, always made in such a way that otherwise hardly visible details might then be observed. These test charts are achieved by tracing series of dividing lines on an ivory blade, each series being subdivided into successive groups, and the millimeter being fractionated into increasingly smaller segments. The line width has to vary from one group to the other in such a proportion that in each and every one of them, the darkened spaces are equally as wide as the gap between them. When such a chart placed at a distance is observed with the unaided eye or an inadequate optical instrument, the various groups only display a grey, uniform colour. If, however, the said distance is reduced or more appropriate instruments are used, the subdivided groups with the widest spacings can then be observed as separate lines, while the rest remains indistinct. By increasing the magnification and shedding sufficient light on the chart, it is ascertained that the said indistinctness of the lines in the groups remaining consistently grey was not imputable to any eye deficiency ; therefore the blame must be put on the instrument alone, which focuses on one group and not on the other. By finding in so doing the group whose subdividing lines are found almost imperceptible because of their close spacing, proof is made that the instrument distinguishes the segments that are separated by a precise angular spacing, but does not separate out those spaced more closely. Hence it follows that the instrument’s ability to penetrate the details of observed objects – in other words, what can be called its “optical power” – is inversely proportional to the critical angle of separability of contiguous segments : in short, it can be described as the quotient of the test chart distance by the average interval of the last discernible lines.”

It must be noted that Guillaume Bigourdan (1851-1932), another brilliant French astronomer, made his own contribution to the instrument’s efficiency, through his representation of the very same patterns, though angled at 45° to reveal a potential problem of astigmatism. Thereby, he considerably spread the use of test charts represented this way.

At first sight, Foucault resolution charts as represented by Bigourdan are not tools intended for the movie industry, nor for camera tests. Instead, they were designed to characterise the visual acuity of mankind’s only natural optical apparatus – the human eye – for an object placed ten meters away.

Bigourdan’s first explanation regarding the charts went as follows :

**" The numbers give, in ****twentieths of millimeters, the distance in between axes of two consecutive black lines (or white ****lines). Thereby, they give, in seconds of arc, the angular distance of these axes, from a distance of ten meters ".**

The degree (°) is the base unit for angle measurement: a right angle is 90°, and a full circle is 360°. An angle of 1° can be divided into subunits: 1° is therefore composed of 60 minutes of arc, each subdivided in 60 seconds of arc. A minute of arc therefore equals 1/60°, that is to say 0,0166°, and a second of arc equals 1/3600°.

Even though the numbering of a P.A.T. chart was initially designed to measure the visual acuity of the human eye at a distance of 10 meters, it can be used just as well in practice for camera tests, to check timing and definition, with any camera system and from any distance.

P.A.T. therefore decided to simplify this technical explanation based on seconds of arc, which, though quite useful in many instances of optical testing, are nonetheless somewhat complex in most cases of application. “The numbers on the targets stand for, in twentieths of millimeter, the number of line pairs imprinted on 1 millimeter”.

The numbers clarification consequently goes as follows :

**“The numbers on the targets stand for, in twentieths of millimeter, the number of line pairs imprinted on 1 millimeter”.**

The degree of sharpness will then depend on the distinctness in between the black lines, and the resolution power on the number of lines observed.

So as to provide you with the best handling possible, P.A.T. offers you a correlation table, which indicates the correspondence relation between : the numbers on the charts, the line pairs and the millimeters imprinted on the chart, the line pairs and the millimeters imprinted on your sensor at a test distance of fifty times the focal length.

*Filming the chart at distance 50 times the focal lenght*

Chart number | Pairs of lines / mm on the chart | Pairs of lines / mm on the sensor |

4 | 5 | 250 |

5 | 4 | 200 |

6 | 3,333 | 166,667 |

7 | 2,857 | 142,857 |

8 | 2,5 | 125 |

9 | 2,222 | 111,111 |

10 | 2 | 100 |

11 | 1,818 | 90,909 |

12 | 1,666 | 83,333 |

13 | 1,538 | 76,923 |

14 | 1,429 | 71,429 |

15 | 1,333 | 66,666 |

16 | 1,25 | 62,5 |

17 | 1,176 | 58,824 |

18 | 1,111 | 55,555 |

19 | 1,053 | 52,632 |

20 | 1 | 50 |

21 | 0,952 | 47,619 |

22 | 0,909 | 45,455 |

23 | 0,87 | 43,478 |

24 | 0,833 | 41,666 |

25 | 0,8 | 40 |

26 | 0,769 | 38,462 |

27 | 0,741 | 37,037 |

28 | 0,714 | 35,714 |

29 | 0,69 | 34,483 |

30 | 0,666 | 33,333 |

31 | 0,645 | 32,258 |

32 | 0,625 | 31,25 |

33 | 0,606 | 30,303 |

34 | 0,589 | 29,412 |

35 | 0,571 | 28,571 |

36 | 0,555 | 27,777 |

37 | 0,541 | 27,027 |

38 | 0,526 | 26,316 |

39 | 0,513 | 25,641 |

40 | 0,5 | 25 |

41 | 0,488 | 24,39 |

42 | 0,476 | 23,81 |

43 | 0,465 | 23,256 |

44 | 0,455 | 22,727 |

45 | 0,444 | 22,222 |

46 | 0,435 | 21,739 |

47 | 0,426 | 21,277 |

48 | 0,417 | 20,833 |

49 | 0,408 | 20,408 |

50 | 0,4 | 20 |

55 | 0,364 | 18,182 |