Using a mandoline with the slicing blade adjusted to the narrowest setting, cut the potatoes into wafer-thin slices, about 1/8-inch thick. (If you do not have a mandoline, carefully use a very sharp knife.)

Soak the sweet potatoes and the Idaho potatoes in separate bowls of ice water at least three hours or overnight in the refrigerator.

Preheat oven to 300 degrees. Heat the vegetable oil in a deep-fat fryer. Drain the potatoes and pat them dry. Fry the sweet potatoes and Idaho potatoes separately in batches in the hot oil until crisp. Drain on paper towels and sprinkle with salt. (You can also sprinkle them with dried herbs or spices.)

To keep chips very crisp, spread them out on a baking sheet and place in the oven while you fry the remaining chips.