My interest in photography led me to study the Scheimpflug principle, which allows control of the plane of focus and the depth of field in your images by tilting or shifting your lens. But I wanted to know the origins and who invented this principle? In this blog post, I will tell the story of Theodor Scheimpflug, an Austrian army captain who devised a method and apparatus for correcting perspective distortion in aerial photographs, and how his discovery influenced photography and optics.

**Who was Theodor Scheimpflug?**

Theodor Scheimpflug was born on October 7, 1865, in Vienna. He attended university in Vienna and joined the Austrian army as an engineer. He became interested in photography and started working on aerial photography in 1902. He realized that conventional cameras could not capture accurate images of oblique objects, such as buildings or mountains, because they would appear distorted due to the lens’s angle of view. He wanted to find a way to correct this distortion and make the images more realistic and proportional.

**What did he invent?**

Scheimpflug invented a device that consisted of a camera with a movable lens and a movable film holder. He attached this device to a balloon or an airplane and took photographs of the landscape from different angles. He then used a mathematical formula to calculate the optimal position of the lens and the film holder for each photograph so that the plane of focus would be parallel to the plane of the object. This way, he could eliminate perspective distortion and achieve sharp focus on things at different distances from the camera.

He patented his invention in 1904 and named it “Apparatus for Correcting Perspective Distortion in Aerial Photographs.” He also published several papers and books on his method and its applications. He credited Jules Carpentier, a French engineer and inventor, for discovering the rule that governed his invention, which he called “Carpentier’s rule.” This rule stated that if the lens, film, and object planes are not parallel, they will intersect at a standard line. This line is called the “Scheimpflug line.”

**How did his invention influence photography and optics?**

Scheimpflug’s invention was a breakthrough in aerial photography and cartography. It allowed him to create accurate maps and surveys of large land areas with minimal distortion. His method was also used for military purposes, such as reconnaissance and artillery targeting. His invention also inspired other photographers and optical engineers to explore the possibilities of tilting or shifting lenses for artistic or scientific purposes.

One of the most famous applications of Scheimpflug’s principle is tilt-shift photography. This technique uses a particular lens type or a digital manipulation program to create selective focus or blur effects in images. This can create an illusion that the captured scene is a miniature model rather than a full-scale environment. Tilt-shift photography is often used for architectural, product, or landscape photography.

**Conclusion**

The Scheimpflug principle is a concept that has revolutionized photography and optics by allowing photographers and optical engineers to control the plane of focus and correct perspective distortion in images.

Now, if that wasn’t enough to put you on the edge of your seat, there is the …

Scheimpflug formula is a term that can refer to different mathematical formulas that are used to apply the Scheimpflug principle in photography and optics. The Scheimpflug principle states that if the lens, image, and subject planes are not parallel, they will intersect at a standard line. This allows for a sharp focus on objects at different distances from the camera by tilting or shifting the lens.

Some of the standard Scheimpflug formulas are:

- The imaging formula: This formula relates the distance of the object plane (z) and the image plane (z’) to the focal length of the lens (f) when they are parallel to each other. It is given by −1= z’z. (1) f
- The Lensmaker’s formula: This formula relates the distance of the object plane (z) and the image plane (z’) to the focal length of the lens (f) when they are not parallel to each other. It is given by −1=1. (2) z’ (y)z(y)f where y is the coordinate along the Scheimpflug line.
- The angle of tilt formula: This formula relates the angle of tilt of the lens plane (θ) and the image plane (θ’) to the focal length of the lens (f) and the distance of the lens from the image plane (L’). It is given by tanθ’=ftanθ. (9) +f
- The magnification formula: This formula relates the magnification of the axial object and image points (mo) and the magnification as a function of y (m) to the angle of tilt of the lens plane (θ), the focal length of the lens (f), and the distance of the lens from the image plane (L’). It is given by mo=L’=f. (10) LL+f and m=mo1+tanθf+L + \uF8F9 \uF04B \uF8FA. (13) \uF8FB

These formulas can be used to calculate the optimal position and orientation of the lens and the image plane for a given subject plane, according to the Scheimpflug principle. They can also be used to calculate the depth of field, perspective correction, and image keystone distortion.

To sum it up, this is computational photography on the next level.