In my experience, there are many things that you need to have a great looking headshot. As an actor though, you should thoroughly research and be sure that your photographer will be able to provide these things.
1. Great lighting. You need great lighting that makes your face pop off the image. It has to really make you stand out from the background.
2. A nice blurred background, or one that supports the type of character you are going for.
3. A shot that brings out the character that you are going for. The truth is that a headshot is not meant to be used overall for all roles. You want a bunch of different looks that you can send out for each role. Remember: casting directors don't have much of an imagination, so you should try to give them something as close to what they are looking for as possible.
4. Something to make your headshot stand out. You gotta make your headshot memorable. Think about what you can do to make yours different. It's like branding yourself. If you can make yourself look different in a way, people will more easily remember you. The headshot photographer can do this also with the type of shot or angle, but remember to ask them ahead of time. This is a thin line to walk: you don't want to be too different that you headshot is no longer a valid one, but you also want to keep it memorable. Tread carefully. You need a really good photographer to get this.
These four points are essential to getting a good headshot, so be sure your photographer can do this. I know I can, just email me at firstname.lastname@example.org.
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