I generally use an "ashtray" analogy to describe the differences between "hard" and "soft" progressive lens design philosophies...
Imagine a clear ashtray. For every diopter of addition power, a scoop of white sand must be dumped into this ashtray. This sand represents unwanted astigmatism and distortion.
Now, the progressive lens designer's problem is to distribute this sand in the most optimum way to provide useful distance, intermediate, and near vision.
The sand can be pushed to either side as much as possible to produce wide fields of clear vision. However, the piles of sand are extremely high in this case, resulting in significant blur and distortion in the periphery. This represents a "hard" design.
Alternatively, the sand can be spread over both sides of the ashtray to produce less blur and distortion in the periphery. However, the sand covers more of the ashtray in this case, resulting in significantly narrower fields of clear view. This represents a "soft" design.
That said, most modern progressive lens designs are neither strictly "hard" nor "soft." Instead, modern progressive lenses often seek to reach the best balance between both lens design philosophies.
You might also find the following articles on progressive lens design helpful:
Progress in the Spectacle Correction of Presbyopia and
Fundamentals of Progressive Lenses.
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