Three elements of depth of field (aperture, focal length, object distance) and real background blur amount control: circle of confusion, out-of-focus spot and blur level

1. The physical optical nature of depth of field and blur: Circle of Confusion model

In absolute geometric optics, only points located on the precise object distance plane can be converged into an ideal geometric light point without area after being refracted by a perfect lens on the sensor surface. All object points located before or after the object distance plane appear as a diffused circular light spot on the sensor:

1. Permissible Circle of Confusion (CoC):

• The resolution of the human eye is limited (it can resolve approximately 1 arcminute at a photopic distance);
• When the spot diameter on the sensor is smaller than a certain physical threshold (usually set at about 0.030mm for full frame and about 0.019mm for APS-C), the human eye still thinks it is a 'clear and sharp point' when observing the enlarged photo with the naked eye;
• The definition of Depth of Field (DoF): the sum of the spatial distances of all objects before and after the focus point, and the spot diameter is smaller than the allowable circle of confusion!

2. Blur Disc Diameter:

• For background objects beyond the depth of field, the diffuse spots expand sharply, the edges and details of the objects are completely smeared and blended, and the originally messy branches, crowds, and telephone poles are softened into beautiful cream-like blocks of color.

2. Comparison of nonlinear decisive weights of the three elements of depth of field

The three physical variables that determine the shallowness of the depth of field and the intensity of the blur have completely different mathematical influence weights:

1. Subject Distance - has the largest weight and has an inverse square relationship!):

• Rule: The closer the camera is to the subject, the depth of field plummets like a cliff; the farther the camera is from the subject, the depth of field expands dramatically on a square scale!
• Practical Reflection: Why is it that when the 50mm f/1.4 is held close to the face to take a close-up, the eyelashes are clear but the ears are blurred, but when the 50mm f/1.4 is held back to take a full-body photo, the background is almost completely blurry? Precisely because the object distance is lengthened 10 times, the depth of field is magnified 100 times!

2. Physical focal length (Focal Length - a square-level relationship!):

• Rule: The longer the focal length, the shallower the depth of field. The angle of view of the background is greatly magnified and compressed by the telephoto, and the out-of-focus spot area is huge;
• Practical Reflection: When shooting full-body portraits, a 200mm f/4 telephoto lens has far better background blur stripping capabilities and space compression than a 50mm f/1.8! Because 200mm drastically zooms in on the distant background and magnifies it 4 times, making the originally tiny circle of confusion look huge;

3. Relative aperture value (Aperture Value - linear relationship):

• Rule: The smaller the f-number of the aperture (the larger the effective physical aperture of light), the steeper the cone angle of the incident light, the faster the diffusion circle, and the shallower the depth of field; when the aperture becomes smaller (such as f/8, f/16), the light cone becomes gentler and the depth of field becomes deeper.

3. Practical operation of "three-step method" for ultimate blurring and subject separation

There is no need to spend tens of thousands of yuan to buy a super large aperture fixed focus, and the secret to shooting air-cut blur with an ordinary lens is:

• Step 1: Bring the subject closer to the lens (zoom in the object distance): As long as the composition allows, bring the camera as close as possible to the person or flower being photographed, and reduce the object distance to the nearest shooting distance;
• Step 2: Move the background away from the subject (increase the depth of field and back distance): Observe the background so that there is a physical distance of at least 5 to 10 meters between the subject and the woods and buildings behind him; the farther the background is from the subject, the larger the circle of dispersion that falls out of focus;
• Step 3: Turn to the longest focal length + open to the maximum aperture: For example, when using a 24-105mm f/4 lens, do not shoot with 24mm. Firmly turn it to the 105mm telephoto end and open the aperture to a constant f/4. In conjunction with the first two steps, you will immediately get a stunning, sharp and smooth blurred blockbuster!

4. Guide to Appreciating Bokeh Quality and Avoiding Pitfalls

Not all blur is beautiful, the ‘texture’ of the blur reflects the optical engineering level of the lens:

1. Smooth Bokeh: High-quality portrait lenses (such as Sony 85mm GM, Canon 85mm f/1.2L) have smooth attenuation of light intensity from the center to the edge of the diffusion circle, without bright hard edges, and the background transitions naturally like melted ice cream;
2. Nisen Bokeh: The spherical aberration of cheap lenses or old double-Gaussian lenses is excessively corrected, and the edge of the circle of confusion presents a high-contrast bright halo (like an onion ring or the edge of a donut), causing the branches and lines in the background to overlap into messy lines with confusing ghost images, which is dizzying;
3. Aperture Eclipse and Cat's Eye Bokeh: Due to mechanical blocking by the edges of the front and rear barrels of the lens, the spots at the edge of the picture are squeezed from a perfect circle into an olive or almond shape, accompanied by a Swirly Bokeh flavor. By reducing the aperture by one stop, the aperture eclipse can be significantly eliminated and the pure circular spot can be restored.