To make chips, place potatoes in a saucepan of cold salted water. Bring to the boil and cook for 2 minutes. Drain. Arrange chips on a cooling rack in a single layer. Refrigerate until cold.
Meanwhile, to make sauce, place cream and zest in a saucepan over low heat until simmering and slightly thickened. Whisk in juice and butter. Remove from heat. Cool slightly. Add egg yolk, whisking until sauce thickens. Strain into a clean saucepan. Stir in capers and dill. Season.
To continue with chips, heat a deep-fryer to 180C. Working in batches, gently drop chips into the oil and fry until crisp and pale golden. Remove with a slotted spoon and drain on absorbent paper.
Transfer to a baking paper lined tray, in a single layer. Place in freezer for 20 minutes.
To cook salmon, pat skin with absorbent paper to dry. Brush with oil and season with salt.
Heat a non stick frying pan over medium heat. Cook salmon, skin-side down, for about 5 minutes or until skin is golden and very crisp. Turn and cook for a further 2-3 minutes or until cooked as desired.
Deep-fry chips a second time until crisp and dark golden brown. Drain on absorbent paper. Season with salt.