Clarifying Coherent and Incoherent Sum of Plane Waves

[ppoonamk]

Hi everyone,

I understand that in Kohler illumination, each point at the source is converted into a plane wave illuminating the object. From what I understand, the total illumination at the object is the incoherent sum of the plane waves. Suppose my source is an ideal coherent laser i.e He-Ne laser. Is the total illumination at the object just a single plane wave?

Could anyone clarify this for me? I am very confused about the coherent and incoherent sum of plane waves at the object. Thank you

 

[Andy Resnick]

Kohler illumination is a little more than what you stated, but close enough. Using a source with some spatial coherence (the laser has high temporal coherence but lower spatial coherence) will result in 'speckle' at the sample plane from interference. Spatially filtering the laser will, AFAIK, remove speckle.

 

[ppoonamk]

Kohler illumination is a little more than what you stated, but close enough. Using a source with some spatial coherence (the laser has high temporal coherence but lower spatial coherence) will result in 'speckle' at the sample plane from interference. Spatially filtering the laser will, AFAIK, remove speckle.

Hi Andy,

Thank you for your response. I understand how the Kohler illumination reduces speckle. So I am writing this program to model an imaging system. So my problem is with the modelling of the illumination on the object. With a He-Ne laser, is the illuminating beam a coherent sum of plane waves or just a single plane wave?

 

[Andy Resnick]

It depends on what you've done to the beam. If it's a 'raw' Gaussian , then you decompose the field accordingly. If the beam is expanded and clipped by the aperture stop, then your decomposition will be altered. If you've spatially filtered and expanded the beam, then you have close to a single plane wave at the aperture stop.

 

[pmacias]

Hello,

Thank you for your question. Kohler illumination is a technique used in microscopy to achieve uniform and optimal lighting of the specimen being observed. In this technique, the light source is focused into a parallel beam of light, which is then focused onto the specimen through the use of a condenser lens. This results in a uniform and cone-shaped illumination of the specimen.

To answer your question, in the case of an ideal coherent laser as the light source, the total illumination at the object will not be just a single plane wave. The laser beam is still composed of multiple plane waves with different phases and amplitudes. However, due to the coherence of the laser light, these plane waves will interfere constructively, resulting in a single, high-intensity beam. This is known as coherent addition.

In contrast, if the light source is incoherent, such as a standard light bulb, the individual plane waves will have random phases and amplitudes, resulting in incoherent addition at the object. This means that the total illumination will not be a single plane wave, but rather a combination of multiple plane waves with varying intensities and phases.

I hope this clarifies the concept for you. Please let me know if you have any further questions.

Best,