The phrase "austere eye" is correct and usable in written English.
It can be used to describe a perspective or viewpoint that is strict, severe, or lacking in embellishment.
Example: "The artist's austere eye for detail transformed the mundane into something extraordinary."
Alternatives: "stern gaze" or "severe perspective".
Each day the farmer's young son would walk past the portrait and stare into the austere eyes of the great composer.
Until recently, he described himself in Who's Who as a "financial executive," and, indeed, he looks like a bookkeeper — tall, thin, with an austere face, in which severe eyes peer unblinkingly from behind thick glasses.
It is austere, but eye-catching.
Angelina Jolie knows that she can appear to be a bit austere in the public eye, but when she's at home, the brunet beauty says, she relaxes and makes sure to have fun.
Van Gogh's depicts him as an austere, enigmatic character with eyes like a cat's — as he put it, "a simple" Japanese monk "worshipping the eternal Buddha".
The Paço dos Duques de Braganca is an eye-catchingly austere palace — though locals will point out that much of its imperial-Gothic grandeur is a product of a comprehensive 20th-century renovation during the regime of the dictator António de Oliveira Salazar.
We're so used to seeing austere photographs of Beauvoir, her eyes slightly hooded and her mouth set in a straight line, as though she was thinking high-minded thoughts about a complicated thesis.
But she had a long, straight nose, light eyes, high cheekbones, and an austere countenance.
Except for a wide, humorous mouth, his face was austere and a little forbidding, and his eyes were sad.
There are flyers in the shape of candy bars, detergent boxes, and dollar bills, printed in eye-catching neon or in austere black-and-white.
